Question

question
solve for x:
\\(\sqrt{4x + 25} - 5 = -2\\)
answer attempt 1 out of 10
x = input box submit answer

Explanation:

Step1: Isolate the square root term

Add 5 to both sides of the equation $\sqrt{4x + 25}-5=-2$ to get $\sqrt{4x + 25}=-2 + 5$.
Simplifying the right side gives $\sqrt{4x + 25}=3$.

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{4x + 25}=3$ to obtain $(\sqrt{4x + 25})^2=3^2$.
This simplifies to $4x + 25 = 9$.

Step3: Solve for x

Subtract 25 from both sides: $4x=9 - 25$.
Simplifying the right side gives $4x=-16$.
Divide both sides by 4: $x=\frac{-16}{4}$.
Simplifying the fraction gives $x = - 4$.

Step4: Check the solution

Substitute $x=-4$ back into the original equation:
Left side: $\sqrt{4\times(-4)+25}-5=\sqrt{-16 + 25}-5=\sqrt{9}-5=3 - 5=-2$, which matches the right side. So the solution is valid.

Answer:

$x=-4$