Question

solve $x^2 + 2x - 15 = 0$ using the quadratic formula. select the solution(s).

$x = -7$ \t\t\t$x = -5$ \t\t\t$x = -3$ \t\t\t$x = -1$ \t\t\t$x = 0$
$x = 1$ \t\t\t$x = 3$ \t\t\t$x = 5$ \t\t\t$x = 7$ \t\t\tno real solutions

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = 2\), \(c = -15\).

Step2: Quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute \(a = 1\), \(b = 2\), \(c = -15\):
\(x=\frac{-2\pm\sqrt{2^2 - 4(1)(-15)}}{2(1)}\)

Step3: Calculate discriminant

Discriminant: \(b^2 - 4ac = 4 + 60 = 64\)

Step4: Solve for x

\(x=\frac{-2\pm\sqrt{64}}{2}=\frac{-2\pm8}{2}\)
Case 1: \(x=\frac{-2 + 8}{2}=\frac{6}{2}=3\)
Case 2: \(x=\frac{-2 - 8}{2}=\frac{-10}{2}=-5\)

Answer:

\(x = -5\), \(x = 3\) (corresponding to options \(x=-5\) and \(x = 3\))