Question

given: $overline{cd}congoverline{ef}$, $overline{cd}congoverline{fg}$, f is the mid - point of $overline{eg}$. prove: statements. reasons to be chosen from the bank. 1. given 2. given 3. 4. reasons. if $x^{2}+x = 30$, then $x = 5$

Explanation:

Step1: Rearrange the equation

Given \(x^{2}+x = 30\), rewrite it as \(x^{2}+x - 30=0\).

Step2: Factor the quadratic equation

We factor \(x^{2}+x - 30\) into \((x + 6)(x - 5)=0\) since \(-30=-5\times6\) and \(-5 + 6=1\).

Step3: Solve for x

Using the zero - product property, if \((x + 6)(x - 5)=0\), then \(x+6 = 0\) or \(x - 5=0\). So \(x=-6\) or \(x = 5\).

Answer:

\(x=-6\) or \(x = 5\)