complete the equivalent equation for -7x - 60 = x² + 10x. (x + )(x + ) = 0 what are the solutions of -7x…

Explanation:

Step1: Rearrange the equation

First, rewrite the equation $-7x - 60=x^{2}+10x$ in standard quadratic - form $ax^{2}+bx + c = 0$. $x^{2}+10x + 7x+60 = 0$, which simplifies to $x^{2}+17x + 60 = 0$.

Step2: Factor the quadratic equation

We need to find two numbers that multiply to $ac = 60$ and add up to $b = 17$. The numbers are 5 and 12 since $5\times12 = 60$ and $5 + 12=17$. So, $x^{2}+17x + 60=(x + 5)(x + 12)=0$.

Step3: Solve for x

Using the zero - product property, if $(x + 5)(x + 12)=0$, then $x+5 = 0$ or $x + 12=0$. If $x+5 = 0$, then $x=-5$; if $x + 12=0$, then $x=-12$.

Answer:

The equivalent equation is $(x + 5)(x + 12)=0$, and the solutions are $x=-5$ or $x=-12$.