2x^2-4x=21 eching

$$2 { x }^{ 2 } -4x=21$$

x uchun yechish

$$x=\frac{\sqrt{46}}{2}+1\approx 4,391164992$$

$$x=-\frac{\sqrt{46}}{2}+1\approx -2,391164992$$

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.

$$2x^{2}-4x=21$$

Tenglamaning ikkala tarafidan 21 ni ayirish.

$$2x^{2}-4x-21=21-21$$

O‘zidan 21 ayirilsa 0 qoladi.

$$2x^{2}-4x-21=0$$

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 -21 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 2\left(-21\right)}}{2\times 2}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-21\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-21\right)}}{2\times 2}$$

-8 ni -21 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+168}}{2\times 2}$$

16 ni 168 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{184}}{2\times 2}$$

184 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{46}}{2\times 2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{46}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{4±2\sqrt{46}}{4}$$

x=\frac{4±2\sqrt{46}}{4} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{46} ga qo'shish.

$$x=\frac{2\sqrt{46}+4}{4}$$

4+2\sqrt{46} ni 4 ga bo'lish.

$$x=\frac{\sqrt{46}}{2}+1$$

x=\frac{4±2\sqrt{46}}{4} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{46} ni ayirish.

$$x=\frac{4-2\sqrt{46}}{4}$$

4-2\sqrt{46} ni 4 ga bo'lish.

$$x=-\frac{\sqrt{46}}{2}+1$$

Tenglama yechildi.

$$x=\frac{\sqrt{46}}{2}+1 x=-\frac{\sqrt{46}}{2}+1$$

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.

$$2x^{2}-4x=21$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-4x}{2}=\frac{21}{2}$$

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

$$x^{2}+\left(-\frac{4}{2}\right)x=\frac{21}{2}$$

-4 ni 2 ga bo'lish.

$$x^{2}-2x=\frac{21}{2}$$

-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.

$$x^{2}-2x+1=\frac{21}{2}+1$$

\frac{21}{2} ni 1 ga qo'shish.

$$x^{2}-2x+1=\frac{23}{2}$$

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.

$$\left(x-1\right)^{2}=\frac{23}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{23}{2}}$$

Qisqartirish.

$$x-1=\frac{\sqrt{46}}{2} x-1=-\frac{\sqrt{46}}{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{46}}{2}+1 x=-\frac{\sqrt{46}}{2}+1$$