(x+10)(x+10)=25 eching

$$( x + 10 ) ( x + 10 ) = 25$$

x uchun yechish

$$x=-5$$

$$x=-15$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(x+10\right)^{2} hosil qilish uchun x+10 va x+10 ni ko'paytirish.

$$\left(x+10\right)^{2}=25$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+10\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+20x+100=25$$

Ikkala tarafdan 25 ni ayirish.

$$x^{2}+20x+100-25=0$$

75 olish uchun 100 dan 25 ni ayirish.

$$x^{2}+20x+75=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 20 ni b va 75 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\times 75}}{2}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\times 75}}{2}$$

-4 ni 75 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400-300}}{2}$$

400 ni -300 ga qo'shish.

$$x=\frac{-20±\sqrt{100}}{2}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±10}{2}$$

x=\frac{-20±10}{2} tenglamasini yeching, bunda ± musbat. -20 ni 10 ga qo'shish.

$$x=-\frac{10}{2}$$

-10 ni 2 ga bo'lish.

$$x=-5$$

x=\frac{-20±10}{2} tenglamasini yeching, bunda ± manfiy. -20 dan 10 ni ayirish.

$$x=-\frac{30}{2}$$

-30 ni 2 ga bo'lish.

$$x=-15$$

Tenglama yechildi.

$$x=-5 x=-15$$

Kvadratni yakunlash bo'yicha qadamlar

\left(x+10\right)^{2} hosil qilish uchun x+10 va x+10 ni ko'paytirish.

$$\left(x+10\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x+10=5 x+10=-5$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$x=-5 x=-15$$