use the zero product property to find the solutions to the equation $x^{2}+12 = 7x$.\n$x=-4$ or $x =…

Explanation:

Step1: Rearrange the equation

First, rewrite the equation $x^{2}+12 = 7x$ in standard quadratic - form $ax^{2}+bx + c = 0$. So, $x^{2}-7x + 12=0$.

Step2: Factor the quadratic equation

We need to find two numbers that multiply to $ac = 1\times12 = 12$ and add up to $b=-7$. The numbers are $-3$ and $-4$. So, $x^{2}-7x + 12=(x - 3)(x - 4)=0$.

Step3: Apply the zero - product property

The zero - product property states that if $ab = 0$, then either $a = 0$ or $b = 0$. So, if $(x - 3)(x - 4)=0$, then $x-3 = 0$ or $x - 4=0$.

Step4: Solve for x

If $x-3 = 0$, then $x = 3$; if $x - 4=0$, then $x = 4$.

Answer:

$x = 3$ or $x = 4$