Question

solve the quadratic equation.
3x² + 7x + 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 \(a = 3\), \(b = 7\), \(c = 1\).

Step2: Apply quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(x=\frac{-7\pm\sqrt{7^2 - 4\times3\times1}}{2\times3}\)

Step3: Simplify discriminant

Calculate \(b^2 - 4ac = 49 - 12 = 37\)

Step4: Find solutions

\(x=\frac{-7\pm\sqrt{37}}{6}\)

Answer:

\(\frac{-7 + \sqrt{37}}{6}\), \(\frac{-7 - \sqrt{37}}{6}\)