Question

solve the quadratic equation.
$4x^{2}+7x - 1 = 0$
write one exact solution in each box. you can add or remove boxes. if there
re no real solutions, remove all boxes.

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 4\), \(b = 7\), \(c = -1\).

Step2: Use quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Calculate discriminant: \(b^2 - 4ac = 7^2 - 4\times4\times(-1)=49 + 16 = 65\)
Substitute into formula: \(x=\frac{-7\pm\sqrt{65}}{2\times4}=\frac{-7\pm\sqrt{65}}{8}\)

Answer:

\(\frac{-7 + \sqrt{65}}{8}\), \(\frac{-7 - \sqrt{65}}{8}\)