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} (2(x+5)^2)/(2)=(52)/(2) \\ \\ (x+5)^2=26 \end{gathered}`

Third, find the square root of both sides:

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

Finally, subtract (5) from both sides

`\begin{gathered} x+5-5=-5\pm√(26) \\ x=-5\pm√(26) \end{gathered}`

So, the answer will be:

`x=\lbrace-5+√(26),-5-√(26)\rbrace`