Question

I need help with a last question I have for my homework and it’s solving by square roots and it’s using quadratic equation

Answer 1

Given the following quadratic equation:

$2(x+5)^2-3=49$

We will solve the equation as follows:

First, add 3 to both sides

$\begin{gathered} 2(x+5)^2-3+3=49+3 \\ 2(x+5)^2=52 \end{gathered}$

Second, divide both sides by 2

$\begin{gathered} \frac{2(x+5)^2}{2}=\frac{52}{2} \\ \\ (x+5)^2=26 \end{gathered}$

Third, find the square root of both sides:

$\begin{gathered} \sqrt{(x+5)^2}=\pm\sqrt{26} \\ x+5=\pm\sqrt{26} \end{gathered}$

Finally, subtract (5) from both sides

$\begin{gathered} x+5-5=-5\pm\sqrt{26} \\ x=-5\pm\sqrt{26} \end{gathered}$

So, the answer will be:

$x=\lbrace-5+\sqrt{26},-5-\sqrt{26}\rbrace$