Question

4x² + 32x = 36

Explanation:

Step1: Simplify the equation

Divide the entire equation \(4x^{2}+32x = 36\) by 4 to simplify. We get \(x^{2}+8x=9\).

Step2: Complete the square

Rewrite the left side as a perfect square trinomial. Take half of the coefficient of \(x\) (which is 8), square it (\((\frac{8}{2})^{2}=16\)), and add it to both sides of the equation. So \(x^{2}+8x + 16=9 + 16\).

Step3: Factor and solve

The left side factors to \((x + 4)^{2}\), and the right side is 25. So \((x + 4)^{2}=25\). Take the square root of both sides: \(x + 4=\pm5\).
For \(x + 4 = 5\), we get \(x=5 - 4=1\).
For \(x + 4=-5\), we get \(x=-5 - 4=-9\).

Answer:

The solutions are \(x = 1\) and \(x=-9\)