Question

use the quadratic formula to solve. express your answer in simplest form. 6w² + w - 15 = 0

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 6\), \(b = 1\), \(c = -15\).

Step2: Quadratic formula

Quadratic formula: \(w=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(w=\frac{-1\pm\sqrt{1^2 - 4\times6\times(-15)}}{2\times6}\)

Step3: Calculate discriminant

Discriminant: \(1 - 4\times6\times(-15)=1 + 360 = 361\)

Step4: Simplify square root

\(\sqrt{361}=19\)

Step5: Solve for w

\(w=\frac{-1\pm19}{12}\)
Two solutions:
\(w_1=\frac{-1 + 19}{12}=\frac{18}{12}=\frac{3}{2}\)
\(w_2=\frac{-1 - 19}{12}=\frac{-20}{12}=-\frac{5}{3}\)

Answer:

\(w = \frac{3}{2}\) or \(w = -\frac{5}{3}\)