Question

1. solve the equation using the quadratic formula.

$x^2 - 2x - 35 = 0$
the solution set is \boxed{}.
(simplify your answer. type an exact answer, using radicals and i as needed. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = -2\), \(c = -35\).

Step2: Apply quadratic formula

Quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Substitute values: \(x=\frac{-(-2)\pm\sqrt{(-2)^2 - 4\times1\times(-35)}}{2\times1}\).

Step3: Simplify the expression

First, calculate discriminant: \((-2)^2 - 4\times1\times(-35)=4 + 140 = 144\).
Then, \(x=\frac{2\pm\sqrt{144}}{2}=\frac{2\pm12}{2}\).

Step4: Find two solutions

For \(+\) sign: \(x=\frac{2 + 12}{2}=\frac{14}{2}=7\).
For \(-\) sign: \(x=\frac{2 - 12}{2}=\frac{-10}{2}=-5\).

Answer:

\(7, -5\)