Question

what is the solution set for the equation?
x² -10x + 36 = 2

○ 3 ± i√11
○ 5 ± 3i
○ 5 ± i√58
○ 10 ± 6i

Explanation:

Step1: Simplify the equation

Subtract 2 from both sides: \(x^2 - 10x + 36 - 2 = 0\)
Simplify: \(x^2 - 10x + 34 = 0\)

Step2: Use the quadratic formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 1\), \(b=-10\), \(c = 34\).
Calculate the discriminant: \(b^2 - 4ac=(-10)^2 - 4\times1\times34 = 100 - 136=-36\)
Then \(x=\frac{10\pm\sqrt{-36}}{2}=\frac{10\pm6i}{2}=5\pm3i\)

Answer:

\(5 \pm 3i\) (corresponding to the option: \(5 \pm 3i\))