Question

solve the quadratic equation.
7x² + 3x - 1 = 0
write one exact solution in each box. you can add or remove boxes. if there are no real solutions, remove all boxes.

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 7\), \(b = 3\), \(c = -1\).

Step2: Use quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(x=\frac{-3\pm\sqrt{3^2 - 4\times7\times(-1)}}{2\times7}\)

Step3: Simplify discriminant

Calculate discriminant: \(3^2 - 4\times7\times(-1)=9 + 28 = 37\)

Step4: Find solutions

So \(x=\frac{-3\pm\sqrt{37}}{14}\)

Answer:

\(\frac{-3 + \sqrt{37}}{14}\), \(\frac{-3 - \sqrt{37}}{14}\)