Question

solve for \\(x\\) in the equation \\(x^2 - 10x + 25 = 35\\).

\\(x = 5 \pm 2\sqrt{5}\\)
\\(x = 5 \pm \sqrt{35}\\)
\\(x = 10 \pm 2\sqrt{5}\\)
\\(x = 10 \pm \sqrt{35}\\)

Explanation:

Step1: Write down the given equation

$$x^2 - 10x + 25 = 35$$

Step2: Factor the left side as a perfect square

$$(x - 5)^2 = 35$$

Step3: Take the square root of both sides

$$x - 5 = \pm\sqrt{35}$$

Step4: Solve for \(x\)

$$x = 5 \pm \sqrt{35}$$

Answer:

\(x = 5 \pm \sqrt{35}\)