Question

question
solve the equation for all values of x by completing the square. express your answer in simplest form.

\\( x^2 - 14x + 36 = 0 \\)

answer attempt 1 out of 2
+ additional solution - no solution
\\( x = \\) submit answer

Explanation:

Step1: Move the constant term to the right

Subtract 36 from both sides of the equation \(x^{2}-14x + 36=0\) to get \(x^{2}-14x=- 36\).

Step2: Complete the square

Take half of the coefficient of \(x\) (which is \(-14\)), so \(\frac{-14}{2}=-7\), then square it: \((-7)^{2} = 49\). Add this to both sides of the equation: \(x^{2}-14x + 49=-36 + 49\).

Step3: Simplify both sides

The left side is a perfect square trinomial, so \((x - 7)^{2}=13\).

Step4: Solve for x

Take the square root of both sides: \(x - 7=\pm\sqrt{13}\). Then add 7 to both sides: \(x=7\pm\sqrt{13}\).

Answer:

\(x = 7+\sqrt{13}\) or \(x = 7-\sqrt{13}\)