(x+9)(x+9)=19 eching

$$(x+9)(x+9)=19$$

x uchun yechish

$$x=\sqrt{19}-9\approx -4,641101056$$

$$x=-\left(\sqrt{19}+9\right)\approx -13,358898944$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(x+9\right)^{2} hosil qilish uchun x+9 va x+9 ni ko'paytirish.

$$\left(x+9\right)^{2}=19$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+9\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+18x+81=19$$

Ikkala tarafdan 19 ni ayirish.

$$x^{2}+18x+81-19=0$$

62 olish uchun 81 dan 19 ni ayirish.

$$x^{2}+18x+62=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 18 ni b va 62 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\times 62}}{2}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\times 62}}{2}$$

-4 ni 62 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-248}}{2}$$

324 ni -248 ga qo'shish.

$$x=\frac{-18±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±2\sqrt{19}}{2}$$

x=\frac{-18±2\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. -18 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}-18}{2}$$

-18+2\sqrt{19} ni 2 ga bo'lish.

$$x=\sqrt{19}-9$$

x=\frac{-18±2\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. -18 dan 2\sqrt{19} ni ayirish.

$$x=\frac{-2\sqrt{19}-18}{2}$$

-18-2\sqrt{19} ni 2 ga bo'lish.

$$x=-\sqrt{19}-9$$

Tenglama yechildi.

$$x=\sqrt{19}-9 x=-\sqrt{19}-9$$

Kvadratni yakunlash bo'yicha qadamlar

\left(x+9\right)^{2} hosil qilish uchun x+9 va x+9 ni ko'paytirish.

$$\left(x+9\right)^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{19}$$

Qisqartirish.

$$x+9=\sqrt{19} x+9=-\sqrt{19}$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x=\sqrt{19}-9 x=-\sqrt{19}-9$$