7x+x^2=(x^2+14x+48)div2 eching

$$7x+ { x }^{ 2 } =( { x }^{ 2 } +14x+48) \div 2$$

x uchun yechish

$$x=4\sqrt{3}\approx 6,92820323$$

$$x=-4\sqrt{3}\approx -6,92820323$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$14x+2x^{2}=x^{2}+14x+48$$

Ikkala tarafdan x^{2} ni ayirish.

$$14x+2x^{2}-x^{2}=14x+48$$

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

$$14x+x^{2}=14x+48$$

Ikkala tarafdan 14x ni ayirish.

$$14x+x^{2}-14x=48$$

0 ni olish uchun 14x va -14x ni birlashtirish.

$$x^{2}=48$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4\sqrt{3} x=-4\sqrt{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$14x+2x^{2}=x^{2}+14x+48$$

Ikkala tarafdan x^{2} ni ayirish.

$$14x+2x^{2}-x^{2}=14x+48$$

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

$$14x+x^{2}=14x+48$$

Ikkala tarafdan 14x ni ayirish.

$$14x+x^{2}-14x=48$$

0 ni olish uchun 14x va -14x ni birlashtirish.

$$x^{2}=48$$

Ikkala tarafdan 48 ni ayirish.

$$x^{2}-48=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -48 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-48\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-48\right)}}{2}$$

-4 ni -48 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{192}}{2}$$

192 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{3}}{2}$$

x=\frac{0±8\sqrt{3}}{2} tenglamasini yeching, bunda ± musbat.

$$x=4\sqrt{3}$$

x=\frac{0±8\sqrt{3}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-4\sqrt{3}$$

Tenglama yechildi.

$$x=4\sqrt{3} x=-4\sqrt{3}$$