(20-5x)(6-x)=125*6 eching

$$( 20 - 5 x ) ( 6 - x ) = 125 \times 6$$

x uchun yechish

$$x=\sqrt{151}+5\approx 17,288205727$$

$$x=5-\sqrt{151}\approx -7,288205727$$

Kvadrat tenglamalaridan foydalanish qoidalari

20-5x ga 6-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$120-50x+5x^{2}=125\times 6$$

750 hosil qilish uchun 125 va 6 ni ko'paytirish.

$$120-50x+5x^{2}=750$$

Ikkala tarafdan 750 ni ayirish.

$$120-50x+5x^{2}-750=0$$

-630 olish uchun 120 dan 750 ni ayirish.

$$-630-50x+5x^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$5x^{2}-50x-630=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -50 ni b va -630 ni c bilan almashtiring.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 5\left(-630\right)}}{2\times 5}$$

-50 kvadratini chiqarish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 5\left(-630\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-20\left(-630\right)}}{2\times 5}$$

-20 ni -630 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500+12600}}{2\times 5}$$

2500 ni 12600 ga qo'shish.

$$x=\frac{-\left(-50\right)±\sqrt{15100}}{2\times 5}$$

15100 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-50\right)±10\sqrt{151}}{2\times 5}$$

-50 ning teskarisi 50 ga teng.

$$x=\frac{50±10\sqrt{151}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{50±10\sqrt{151}}{10}$$

x=\frac{50±10\sqrt{151}}{10} tenglamasini yeching, bunda ± musbat. 50 ni 10\sqrt{151} ga qo'shish.

$$x=\frac{10\sqrt{151}+50}{10}$$

50+10\sqrt{151} ni 10 ga bo'lish.

$$x=\sqrt{151}+5$$

x=\frac{50±10\sqrt{151}}{10} tenglamasini yeching, bunda ± manfiy. 50 dan 10\sqrt{151} ni ayirish.

$$x=\frac{50-10\sqrt{151}}{10}$$

50-10\sqrt{151} ni 10 ga bo'lish.

$$x=5-\sqrt{151}$$

Tenglama yechildi.

$$x=\sqrt{151}+5 x=5-\sqrt{151}$$

Kvadratni yakunlash bo'yicha qadamlar

20-5x ga 6-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$120-50x+5x^{2}=125\times 6$$

750 hosil qilish uchun 125 va 6 ni ko'paytirish.

$$120-50x+5x^{2}=750$$

Ikkala tarafdan 120 ni ayirish.

$$-50x+5x^{2}=750-120$$

630 olish uchun 750 dan 120 ni ayirish.

$$-50x+5x^{2}=630$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$5x^{2}-50x=630$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-50x}{5}=\frac{630}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{50}{5}\right)x=\frac{630}{5}$$

-50 ni 5 ga bo'lish.

$$x^{2}-10x=\frac{630}{5}$$

630 ni 5 ga bo'lish.

$$x^{2}-10x=126$$

-10 ni bo‘lish, x shartining koeffitsienti, 2 ga -5 olish uchun. Keyin, -5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-10x+\left(-5\right)^{2}=126+\left(-5\right)^{2}$$

-5 kvadratini chiqarish.

$$x^{2}-10x+25=126+25$$

126 ni 25 ga qo'shish.

$$x^{2}-10x+25=151$$

x^{2}-10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-5\right)^{2}=151$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{151}$$

Qisqartirish.

$$x-5=\sqrt{151} x-5=-\sqrt{151}$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{151}+5 x=5-\sqrt{151}$$