-2x^2+7x+6=0 eching

$$- 2 x ^ { 2 } + 7 x + 6 = 0$$

x uchun yechish

$$x = \frac{\sqrt{97} + 7}{4} \approx 4,21221445$$

$$x=\frac{7-\sqrt{97}}{4}\approx -0,71221445$$

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.

$$-2x^{2}+7x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 7 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+8\times 6}}{2\left(-2\right)}$$

8 ni 6 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+48}}{2\left(-2\right)}$$

49 ni 48 ga qo'shish.

$$x=\frac{-7±\sqrt{97}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{97}}{-4}$$

x=\frac{-7±\sqrt{97}}{-4} tenglamasini yeching, bunda ± musbat. -7 ni \sqrt{97} ga qo'shish.

$$x=\frac{\sqrt{97}-7}{-4}$$

-7+\sqrt{97} ni -4 ga bo'lish.

$$x=\frac{7-\sqrt{97}}{4}$$

x=\frac{-7±\sqrt{97}}{-4} tenglamasini yeching, bunda ± manfiy. -7 dan \sqrt{97} ni ayirish.

$$x=\frac{-\sqrt{97}-7}{-4}$$

-7-\sqrt{97} ni -4 ga bo'lish.

$$x=\frac{\sqrt{97}+7}{4}$$

Tenglama yechildi.

$$x=\frac{7-\sqrt{97}}{4} x=\frac{\sqrt{97}+7}{4}$$

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.

$$-2x^{2}+7x+6=0$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$-2x^{2}+7x+6-6=-6$$

O‘zidan 6 ayirilsa 0 qoladi.

$$-2x^{2}+7x=-6$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+7x}{-2}=-\frac{6}{-2}$$

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

$$x^{2}+\frac{7}{-2}x=-\frac{6}{-2}$$

7 ni -2 ga bo'lish.

$$x^{2}-\frac{7}{2}x=-\frac{6}{-2}$$

-6 ni -2 ga bo'lish.

$$x^{2}-\frac{7}{2}x=3$$

-\frac{7}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{4} olish uchun. Keyin, -\frac{7}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{7}{2}x+\left(-\frac{7}{4}\right)^{2}=3+\left(-\frac{7}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{4} kvadratini chiqarish.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=3+\frac{49}{16}$$

3 ni \frac{49}{16} ga qo'shish.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=\frac{97}{16}$$

x^{2}-\frac{7}{2}x+\frac{49}{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.

$$\left(x-\frac{7}{4}\right)^{2}=\frac{97}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{4}\right)^{2}}=\sqrt{\frac{97}{16}}$$

Qisqartirish.

$$x-\frac{7}{4}=\frac{\sqrt{97}}{4} x-\frac{7}{4}=-\frac{\sqrt{97}}{4}$$

\frac{7}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{97}+7}{4} x=\frac{7-\sqrt{97}}{4}$$