20x=64-2(x^2 eching

$$20x=64-2( { x }^{ 2 }$$

x uchun yechish (complex solution)

$$x=\sqrt{57}-5\approx 2,549834435$$

$$x=-\left(\sqrt{57}+5\right)\approx -12,549834435$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 64 ni ayirish.

$$20x-64=-2x^{2}$$

2x^{2} ni ikki tarafga qo’shing.

$$20x-64+2x^{2}=0$$

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.

$$2x^{2}+20x-64=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 20 ni b va -64 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\times 2\left(-64\right)}}{2\times 2}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\times 2\left(-64\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400-8\left(-64\right)}}{2\times 2}$$

-8 ni -64 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+512}}{2\times 2}$$

400 ni 512 ga qo'shish.

$$x=\frac{-20±\sqrt{912}}{2\times 2}$$

912 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±4\sqrt{57}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-20±4\sqrt{57}}{4}$$

x=\frac{-20±4\sqrt{57}}{4} tenglamasini yeching, bunda ± musbat. -20 ni 4\sqrt{57} ga qo'shish.

$$x=\frac{4\sqrt{57}-20}{4}$$

-20+4\sqrt{57} ni 4 ga bo'lish.

$$x=\sqrt{57}-5$$

x=\frac{-20±4\sqrt{57}}{4} tenglamasini yeching, bunda ± manfiy. -20 dan 4\sqrt{57} ni ayirish.

$$x=\frac{-4\sqrt{57}-20}{4}$$

-20-4\sqrt{57} ni 4 ga bo'lish.

$$x=-\sqrt{57}-5$$

Tenglama yechildi.

$$x=\sqrt{57}-5 x=-\sqrt{57}-5$$

Kvadratni yakunlash bo'yicha qadamlar

2x^{2} ni ikki tarafga qo’shing.

$$20x+2x^{2}=64$$

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

$$2x^{2}+20x=64$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+20x}{2}=\frac{64}{2}$$

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

$$x^{2}+\frac{20}{2}x=\frac{64}{2}$$

20 ni 2 ga bo'lish.

$$x^{2}+10x=\frac{64}{2}$$

64 ni 2 ga bo'lish.

$$x^{2}+10x=32$$

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.

$$x^{2}+10x+5^{2}=32+5^{2}$$

5 kvadratini chiqarish.

$$x^{2}+10x+25=32+25$$

32 ni 25 ga qo'shish.

$$x^{2}+10x+25=57$$

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.

$$\left(x+5\right)^{2}=57$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{57}$$

Qisqartirish.

$$x+5=\sqrt{57} x+5=-\sqrt{57}$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$x=\sqrt{57}-5 x=-\sqrt{57}-5$$

x uchun yechish

$$x=\sqrt{57}-5\approx 2,549834435$$

$$x=-\sqrt{57}-5\approx -12,549834435$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 64 ni ayirish.

$$20x-64=-2x^{2}$$

2x^{2} ni ikki tarafga qo’shing.

$$20x-64+2x^{2}=0$$

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.

$$2x^{2}+20x-64=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 20 ni b va -64 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\times 2\left(-64\right)}}{2\times 2}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\times 2\left(-64\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400-8\left(-64\right)}}{2\times 2}$$

-8 ni -64 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+512}}{2\times 2}$$

400 ni 512 ga qo'shish.

$$x=\frac{-20±\sqrt{912}}{2\times 2}$$

912 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±4\sqrt{57}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-20±4\sqrt{57}}{4}$$

x=\frac{-20±4\sqrt{57}}{4} tenglamasini yeching, bunda ± musbat. -20 ni 4\sqrt{57} ga qo'shish.

$$x=\frac{4\sqrt{57}-20}{4}$$

-20+4\sqrt{57} ni 4 ga bo'lish.

$$x=\sqrt{57}-5$$

x=\frac{-20±4\sqrt{57}}{4} tenglamasini yeching, bunda ± manfiy. -20 dan 4\sqrt{57} ni ayirish.

$$x=\frac{-4\sqrt{57}-20}{4}$$

-20-4\sqrt{57} ni 4 ga bo'lish.

$$x=-\sqrt{57}-5$$

Tenglama yechildi.

$$x=\sqrt{57}-5 x=-\sqrt{57}-5$$

Kvadratni yakunlash bo'yicha qadamlar

2x^{2} ni ikki tarafga qo’shing.

$$20x+2x^{2}=64$$

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

$$2x^{2}+20x=64$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+20x}{2}=\frac{64}{2}$$

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

$$x^{2}+\frac{20}{2}x=\frac{64}{2}$$

20 ni 2 ga bo'lish.

$$x^{2}+10x=\frac{64}{2}$$

64 ni 2 ga bo'lish.

$$x^{2}+10x=32$$

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.

$$x^{2}+10x+5^{2}=32+5^{2}$$

5 kvadratini chiqarish.

$$x^{2}+10x+25=32+25$$

32 ni 25 ga qo'shish.

$$x^{2}+10x+25=57$$

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.

$$\left(x+5\right)^{2}=57$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{57}$$

Qisqartirish.

$$x+5=\sqrt{57} x+5=-\sqrt{57}$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$x=\sqrt{57}-5 x=-\sqrt{57}-5$$