2x^2-4x-135=0 eching

$$2 { x }^{ 2 } -4x-135=0$$

x uchun yechish

$$x=\frac{\sqrt{274}}{2}+1\approx 9,276472679$$

$$x=-\frac{\sqrt{274}}{2}+1\approx -7,276472679$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$2x^{2}-4x-135=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -4 ni b va -135 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 2\left(-135\right)}}{2\times 2}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-135\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-135\right)}}{2\times 2}$$

-8 ni -135 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+1080}}{2\times 2}$$

16 ni 1080 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{1096}}{2\times 2}$$

1096 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{274}}{2\times 2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{274}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{4±2\sqrt{274}}{4}$$

x=\frac{4±2\sqrt{274}}{4} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{274} ga qo'shish.

$$x=\frac{2\sqrt{274}+4}{4}$$

4+2\sqrt{274} ni 4 ga bo'lish.

$$x=\frac{\sqrt{274}}{2}+1$$

x=\frac{4±2\sqrt{274}}{4} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{274} ni ayirish.

$$x=\frac{4-2\sqrt{274}}{4}$$

4-2\sqrt{274} ni 4 ga bo'lish.

$$x=-\frac{\sqrt{274}}{2}+1$$

Tenglama yechildi.

$$x=\frac{\sqrt{274}}{2}+1 x=-\frac{\sqrt{274}}{2}+1$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$2x^{2}-4x-135=0$$

135 ni tenglamaning ikkala tarafiga qo'shish.

$$2x^{2}-4x-135-\left(-135\right)=-\left(-135\right)$$

O‘zidan -135 ayirilsa 0 qoladi.

$$2x^{2}-4x=-\left(-135\right)$$

0 dan -135 ni ayirish.

$$2x^{2}-4x=135$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-4x}{2}=\frac{135}{2}$$

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

$$x^{2}+\left(-\frac{4}{2}\right)x=\frac{135}{2}$$

-4 ni 2 ga bo'lish.

$$x^{2}-2x=\frac{135}{2}$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2x+1=\frac{135}{2}+1$$

\frac{135}{2} ni 1 ga qo'shish.

$$x^{2}-2x+1=\frac{137}{2}$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=\frac{137}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{137}{2}}$$

Qisqartirish.

$$x-1=\frac{\sqrt{274}}{2} x-1=-\frac{\sqrt{274}}{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{274}}{2}+1 x=-\frac{\sqrt{274}}{2}+1$$