85=2x^2-10 eching

$$85 = 2 x ^ { 2 } - 10$$

x uchun yechish

$$x = \frac{\sqrt{190}}{2} \approx 6,892024376$$

$$x = -\frac{\sqrt{190}}{2} \approx -6,892024376$$

Kvadrat ildizini topish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}-10=85$$

10 ni ikki tarafga qo’shing.

$$2x^{2}=85+10$$

95 olish uchun 85 va 10'ni qo'shing.

$$2x^{2}=95$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{95}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{190}}{2} x=-\frac{\sqrt{190}}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}-10=85$$

Ikkala tarafdan 85 ni ayirish.

$$2x^{2}-10-85=0$$

-95 olish uchun -10 dan 85 ni ayirish.

$$2x^{2}-95=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va -95 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-95\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-95\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-95\right)}}{2\times 2}$$

-8 ni -95 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{760}}{2\times 2}$$

760 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{190}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{190}}{4}$$

x=\frac{0±2\sqrt{190}}{4} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{190}}{2}$$

x=\frac{0±2\sqrt{190}}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{190}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{190}}{2} x=-\frac{\sqrt{190}}{2}$$