3/2+2625+3/2/frac{x+25{2}}=300/x+frac{1}{2} eching

$$\frac{ 3 }{ 2 } + \frac{ 2625+ \frac{ 3 }{ 2 } }{ \frac{ x+25 }{ 2 } } = \frac{ 300 }{ x } + \frac{ 1 }{ 2 }$$

x uchun yechish (complex solution)

$$x=\sqrt{6202621}-2489\approx 1,506173451$$

$$x=-\left(\sqrt{6202621}+2489\right)\approx -4979,506173451$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x ga, 2,x ning eng kichik karralisiga ko‘paytiring.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

3 hosil qilish uchun 2 va \frac{3}{2} ni ko'paytirish.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

\frac{5253}{2} olish uchun 2625 va \frac{3}{2}'ni qo'shing.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

10506 hosil qilish uchun 4 va \frac{5253}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

600 hosil qilish uchun 2 va 300 ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

1 hosil qilish uchun 2 va \frac{1}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Ikkala tarafdan 600 ni ayirish.

$$3x+10506x\left(x+25\right)^{-1}-600=x$$

Ikkala tarafdan x ni ayirish.

$$3x+10506x\left(x+25\right)^{-1}-600-x=0$$

2x ni olish uchun 3x va -x ni birlashtirish.

$$2x+10506x\left(x+25\right)^{-1}-600=0$$

Shartlarni qayta saralash.

$$2x+10506\times \frac{1}{x+25}x-600=0$$

x qiymati -25 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+25 ga ko'paytirish.

$$2x\left(x+25\right)+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

2x ga x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+50x+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

10506 hosil qilish uchun 10506 va 1 ni ko'paytirish.

$$2x^{2}+50x+10506x+\left(x+25\right)\left(-600\right)=0$$

10556x ni olish uchun 50x va 10506x ni birlashtirish.

$$2x^{2}+10556x+\left(x+25\right)\left(-600\right)=0$$

x+25 ga -600 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+10556x-600x-15000=0$$

9956x ni olish uchun 10556x va -600x ni birlashtirish.

$$2x^{2}+9956x-15000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 9956 ni b va -15000 ni c bilan almashtiring.

$$x=\frac{-9956±\sqrt{9956^{2}-4\times 2\left(-15000\right)}}{2\times 2}$$

9956 kvadratini chiqarish.

$$x=\frac{-9956±\sqrt{99121936-4\times 2\left(-15000\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-9956±\sqrt{99121936-8\left(-15000\right)}}{2\times 2}$$

-8 ni -15000 marotabaga ko'paytirish.

$$x=\frac{-9956±\sqrt{99121936+120000}}{2\times 2}$$

99121936 ni 120000 ga qo'shish.

$$x=\frac{-9956±\sqrt{99241936}}{2\times 2}$$

99241936 ning kvadrat ildizini chiqarish.

$$x=\frac{-9956±4\sqrt{6202621}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-9956±4\sqrt{6202621}}{4}$$

x=\frac{-9956±4\sqrt{6202621}}{4} tenglamasini yeching, bunda ± musbat. -9956 ni 4\sqrt{6202621} ga qo'shish.

$$x=\frac{4\sqrt{6202621}-9956}{4}$$

-9956+4\sqrt{6202621} ni 4 ga bo'lish.

$$x=\sqrt{6202621}-2489$$

x=\frac{-9956±4\sqrt{6202621}}{4} tenglamasini yeching, bunda ± manfiy. -9956 dan 4\sqrt{6202621} ni ayirish.

$$x=\frac{-4\sqrt{6202621}-9956}{4}$$

-9956-4\sqrt{6202621} ni 4 ga bo'lish.

$$x=-\sqrt{6202621}-2489$$

Tenglama yechildi.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x ga, 2,x ning eng kichik karralisiga ko‘paytiring.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

3 hosil qilish uchun 2 va \frac{3}{2} ni ko'paytirish.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

\frac{5253}{2} olish uchun 2625 va \frac{3}{2}'ni qo'shing.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

10506 hosil qilish uchun 4 va \frac{5253}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

600 hosil qilish uchun 2 va 300 ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

1 hosil qilish uchun 2 va \frac{1}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Ikkala tarafdan x ni ayirish.

$$3x+10506x\left(x+25\right)^{-1}-x=600$$

2x ni olish uchun 3x va -x ni birlashtirish.

$$2x+10506x\left(x+25\right)^{-1}=600$$

Shartlarni qayta saralash.

$$2x+10506\times \frac{1}{x+25}x=600$$

x qiymati -25 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+25 ga ko'paytirish.

$$2x\left(x+25\right)+10506\times 1x=600\left(x+25\right)$$

2x ga x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+50x+10506\times 1x=600\left(x+25\right)$$

10506 hosil qilish uchun 10506 va 1 ni ko'paytirish.

$$2x^{2}+50x+10506x=600\left(x+25\right)$$

10556x ni olish uchun 50x va 10506x ni birlashtirish.

$$2x^{2}+10556x=600\left(x+25\right)$$

600 ga x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+10556x=600x+15000$$

Ikkala tarafdan 600x ni ayirish.

$$2x^{2}+10556x-600x=15000$$

9956x ni olish uchun 10556x va -600x ni birlashtirish.

$$2x^{2}+9956x=15000$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+9956x}{2}=\frac{15000}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{9956}{2}x=\frac{15000}{2}$$

9956 ni 2 ga bo'lish.

$$x^{2}+4978x=\frac{15000}{2}$$

15000 ni 2 ga bo'lish.

$$x^{2}+4978x=7500$$

4978 ni bo‘lish, x shartining koeffitsienti, 2 ga 2489 olish uchun. Keyin, 2489 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+4978x+2489^{2}=7500+2489^{2}$$

2489 kvadratini chiqarish.

$$x^{2}+4978x+6195121=7500+6195121$$

7500 ni 6195121 ga qo'shish.

$$x^{2}+4978x+6195121=6202621$$

x^{2}+4978x+6195121 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+2489\right)^{2}=6202621$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2489\right)^{2}}=\sqrt{6202621}$$

Qisqartirish.

$$x+2489=\sqrt{6202621} x+2489=-\sqrt{6202621}$$

Tenglamaning ikkala tarafidan 2489 ni ayirish.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$

x uchun yechish

$$x=\sqrt{6202621}-2489\approx 1,506173451$$

$$x=-\sqrt{6202621}-2489\approx -4979,506173451$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x ga, 2,x ning eng kichik karralisiga ko‘paytiring.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

3 hosil qilish uchun 2 va \frac{3}{2} ni ko'paytirish.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

\frac{5253}{2} olish uchun 2625 va \frac{3}{2}'ni qo'shing.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

10506 hosil qilish uchun 4 va \frac{5253}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

600 hosil qilish uchun 2 va 300 ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

1 hosil qilish uchun 2 va \frac{1}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Ikkala tarafdan 600 ni ayirish.

$$3x+10506x\left(x+25\right)^{-1}-600=x$$

Ikkala tarafdan x ni ayirish.

$$3x+10506x\left(x+25\right)^{-1}-600-x=0$$

2x ni olish uchun 3x va -x ni birlashtirish.

$$2x+10506x\left(x+25\right)^{-1}-600=0$$

Shartlarni qayta saralash.

$$2x+10506\times \frac{1}{x+25}x-600=0$$

x qiymati -25 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+25 ga ko'paytirish.

$$2x\left(x+25\right)+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

2x ga x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+50x+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

10506 hosil qilish uchun 10506 va 1 ni ko'paytirish.

$$2x^{2}+50x+10506x+\left(x+25\right)\left(-600\right)=0$$

10556x ni olish uchun 50x va 10506x ni birlashtirish.

$$2x^{2}+10556x+\left(x+25\right)\left(-600\right)=0$$

x+25 ga -600 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+10556x-600x-15000=0$$

9956x ni olish uchun 10556x va -600x ni birlashtirish.

$$2x^{2}+9956x-15000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 9956 ni b va -15000 ni c bilan almashtiring.

$$x=\frac{-9956±\sqrt{9956^{2}-4\times 2\left(-15000\right)}}{2\times 2}$$

9956 kvadratini chiqarish.

$$x=\frac{-9956±\sqrt{99121936-4\times 2\left(-15000\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-9956±\sqrt{99121936-8\left(-15000\right)}}{2\times 2}$$

-8 ni -15000 marotabaga ko'paytirish.

$$x=\frac{-9956±\sqrt{99121936+120000}}{2\times 2}$$

99121936 ni 120000 ga qo'shish.

$$x=\frac{-9956±\sqrt{99241936}}{2\times 2}$$

99241936 ning kvadrat ildizini chiqarish.

$$x=\frac{-9956±4\sqrt{6202621}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-9956±4\sqrt{6202621}}{4}$$

x=\frac{-9956±4\sqrt{6202621}}{4} tenglamasini yeching, bunda ± musbat. -9956 ni 4\sqrt{6202621} ga qo'shish.

$$x=\frac{4\sqrt{6202621}-9956}{4}$$

-9956+4\sqrt{6202621} ni 4 ga bo'lish.

$$x=\sqrt{6202621}-2489$$

x=\frac{-9956±4\sqrt{6202621}}{4} tenglamasini yeching, bunda ± manfiy. -9956 dan 4\sqrt{6202621} ni ayirish.

$$x=\frac{-4\sqrt{6202621}-9956}{4}$$

-9956-4\sqrt{6202621} ni 4 ga bo'lish.

$$x=-\sqrt{6202621}-2489$$

Tenglama yechildi.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x ga, 2,x ning eng kichik karralisiga ko‘paytiring.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

3 hosil qilish uchun 2 va \frac{3}{2} ni ko'paytirish.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

\frac{5253}{2} olish uchun 2625 va \frac{3}{2}'ni qo'shing.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

10506 hosil qilish uchun 4 va \frac{5253}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

600 hosil qilish uchun 2 va 300 ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

1 hosil qilish uchun 2 va \frac{1}{2} ni ko'paytirish.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Ikkala tarafdan x ni ayirish.

$$3x+10506x\left(x+25\right)^{-1}-x=600$$

2x ni olish uchun 3x va -x ni birlashtirish.

$$2x+10506x\left(x+25\right)^{-1}=600$$

Shartlarni qayta saralash.

$$2x+10506\times \frac{1}{x+25}x=600$$

x qiymati -25 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+25 ga ko'paytirish.

$$2x\left(x+25\right)+10506\times 1x=600\left(x+25\right)$$

2x ga x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+50x+10506\times 1x=600\left(x+25\right)$$

10506 hosil qilish uchun 10506 va 1 ni ko'paytirish.

$$2x^{2}+50x+10506x=600\left(x+25\right)$$

10556x ni olish uchun 50x va 10506x ni birlashtirish.

$$2x^{2}+10556x=600\left(x+25\right)$$

600 ga x+25 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+10556x=600x+15000$$

Ikkala tarafdan 600x ni ayirish.

$$2x^{2}+10556x-600x=15000$$

9956x ni olish uchun 10556x va -600x ni birlashtirish.

$$2x^{2}+9956x=15000$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+9956x}{2}=\frac{15000}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{9956}{2}x=\frac{15000}{2}$$

9956 ni 2 ga bo'lish.

$$x^{2}+4978x=\frac{15000}{2}$$

15000 ni 2 ga bo'lish.

$$x^{2}+4978x=7500$$

4978 ni bo‘lish, x shartining koeffitsienti, 2 ga 2489 olish uchun. Keyin, 2489 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+4978x+2489^{2}=7500+2489^{2}$$

2489 kvadratini chiqarish.

$$x^{2}+4978x+6195121=7500+6195121$$

7500 ni 6195121 ga qo'shish.

$$x^{2}+4978x+6195121=6202621$$

x^{2}+4978x+6195121 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+2489\right)^{2}=6202621$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2489\right)^{2}}=\sqrt{6202621}$$

Qisqartirish.

$$x+2489=\sqrt{6202621} x+2489=-\sqrt{6202621}$$

Tenglamaning ikkala tarafidan 2489 ni ayirish.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$