Solve the quadratic equation. \[ 7 x^{2}+3 x-1=0 \] Write one exact, simplified solution in each box. You can add or remove boxes. If a solution not a real number, write it in the form a + bi or a - bi, where a and b are real numbers. \begin{tabular}{|c}\( \square \frac{\square}{\square} \)\end{tabular}

Solve the equation \( 7x^2+3x-1=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(7x^{2}+3x-1=0\) - step1: Solve using the quadratic formula: \(x=\frac{-3\pm \sqrt{3^{2}-4\times 7\left(-1\right)}}{2\times 7}\) - step2: Simplify the expression: \(x=\frac{-3\pm \sqrt{3^{2}-4\times 7\left(-1\right)}}{14}\) - step3: Simplify the expression: \(x=\frac{-3\pm \sqrt{37}}{14}\) - step4: Separate into possible cases: \(\begin{align}&x=\frac{-3+\sqrt{37}}{14}\\&x=\frac{-3-\sqrt{37}}{14}\end{align}\) - step5: Rewrite the fraction: \(\begin{align}&x=\frac{-3+\sqrt{37}}{14}\\&x=-\frac{3+\sqrt{37}}{14}\end{align}\) - step6: Rewrite: \(x_{1}=-\frac{3+\sqrt{37}}{14},x_{2}=\frac{-3+\sqrt{37}}{14}\) The solutions to the quadratic equation \(7x^2 + 3x - 1 = 0\) are: \[ x_{1} = -\frac{3 + \sqrt{37}}{14} \] \[ x_{2} = \frac{-3 + \sqrt{37}}{14} \] Therefore, the exact, simplified solutions are: \[ x_{1} = -\frac{3 + \sqrt{37}}{14} \] \[ x_{2} = \frac{-3 + \sqrt{37}}{14} \]