9(x)=2x^2+2x-1/2 eching

$$9 ( x ) = \frac { 2 x ^ { 2 } + 2 x - 1 } { 2 }$$

x uchun yechish

$$x=\frac{\sqrt{66}}{2}+4\approx 8,062019202$$

$$x=-\frac{\sqrt{66}}{2}+4\approx -0,062019202$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$18x=2x^{2}+2x-1$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$18x-2x^{2}=2x-1$$

Ikkala tarafdan 2x ni ayirish.

$$18x-2x^{2}-2x=-1$$

16x ni olish uchun 18x va -2x ni birlashtirish.

$$16x-2x^{2}=-1$$

1 ni ikki tarafga qo’shing.

$$16x-2x^{2}+1=0$$

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.

$$-2x^{2}+16x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 16 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-2\right)}}{2\left(-2\right)}$$

16 kvadratini chiqarish.

$$x=\frac{-16±\sqrt{256-4\left(-2\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-16±\sqrt{256+8}}{2\left(-2\right)}$$

256 ni 8 ga qo'shish.

$$x=\frac{-16±\sqrt{264}}{2\left(-2\right)}$$

264 ning kvadrat ildizini chiqarish.

$$x=\frac{-16±2\sqrt{66}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-16±2\sqrt{66}}{-4}$$

x=\frac{-16±2\sqrt{66}}{-4} tenglamasini yeching, bunda ± musbat. -16 ni 2\sqrt{66} ga qo'shish.

$$x=\frac{2\sqrt{66}-16}{-4}$$

-16+2\sqrt{66} ni -4 ga bo'lish.

$$x=-\frac{\sqrt{66}}{2}+4$$

x=\frac{-16±2\sqrt{66}}{-4} tenglamasini yeching, bunda ± manfiy. -16 dan 2\sqrt{66} ni ayirish.

$$x=\frac{-2\sqrt{66}-16}{-4}$$

-16-2\sqrt{66} ni -4 ga bo'lish.

$$x=\frac{\sqrt{66}}{2}+4$$

Tenglama yechildi.

$$x=-\frac{\sqrt{66}}{2}+4 x=\frac{\sqrt{66}}{2}+4$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$18x=2x^{2}+2x-1$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$18x-2x^{2}=2x-1$$

Ikkala tarafdan 2x ni ayirish.

$$18x-2x^{2}-2x=-1$$

16x ni olish uchun 18x va -2x ni birlashtirish.

$$16x-2x^{2}=-1$$

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

$$-2x^{2}+16x=-1$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+16x}{-2}=-\frac{1}{-2}$$

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

$$x^{2}+\frac{16}{-2}x=-\frac{1}{-2}$$

16 ni -2 ga bo'lish.

$$x^{2}-8x=-\frac{1}{-2}$$

-1 ni -2 ga bo'lish.

$$x^{2}-8x=\frac{1}{2}$$

-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-8x+\left(-4\right)^{2}=\frac{1}{2}+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$x^{2}-8x+16=\frac{1}{2}+16$$

\frac{1}{2} ni 16 ga qo'shish.

$$x^{2}-8x+16=\frac{33}{2}$$

x^{2}-8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-4\right)^{2}=\frac{33}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{\frac{33}{2}}$$

Qisqartirish.

$$x-4=\frac{\sqrt{66}}{2} x-4=-\frac{\sqrt{66}}{2}$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{66}}{2}+4 x=-\frac{\sqrt{66}}{2}+4$$