use the zero product property to find the solutions to the equation $x^{2}+x - 30 = 12$.\n$x=-7$ or $x =…

use the zero product property to find the solutions to the equation $x^{2}+x - 30 = 12$.\n$x=-7$ or $x = 6$\n$x=-7$ or $x=-6$\n$x=-6$ or $x = 7$\n$x = 6$ or $x = 7$

use the zero product property to find the solutions to the equation $x^{2}+x - 30 = 12$.\n$x=-7$ or $x = 6$\n$x=-7$ or $x=-6$\n$x=-6$ or $x = 7$\n$x = 6$ or $x = 7$

Answer

Explanation:

Step1: Rearrange the equation

First, rewrite $x^{2}+x - 30=12$ as $x^{2}+x-42 = 0$.

Step2: Factor the quadratic equation

Factor $x^{2}+x - 42$ into $(x + 7)(x - 6)=0$.

Step3: Apply zero - product property

If $(x + 7)(x - 6)=0$, then $x+7 = 0$ or $x - 6=0$. For $x+7 = 0$, we get $x=-7$. For $x - 6=0$, we get $x = 6$.

Answer:

A. $x=-7$ or $x = 6$