solve the quadratic equation.\n7x² + 3x - 1 = 0\nwrite one exact, simplified solution in each box. you can…

solve the quadratic equation.\n7x² + 3x - 1 = 0\nwrite one exact, simplified solution in each box. you can add or remove boxes. if a solution is not a real number, write it in the form a + bi or a - bi, where a and b are real numbers.

solve the quadratic equation.\n7x² + 3x - 1 = 0\nwrite one exact, simplified solution in each box. you can add or remove boxes. if a solution is not a real number, write it in the form a + bi or a - bi, where a and b are real numbers.

Answer

Explanation:

Step1: Identify coefficients

For the quadratic equation (7x^{2}+3x - 1=0), the coefficients are (a = 7), (b = 3), and (c=-1).

Step2: Calculate discriminant

The discriminant (\Delta=b^{2}-4ac). Substitute (a = 7), (b = 3), (c=-1) into the formula: [ \begin{align*} \Delta&=(3)^{2}-4\times7\times(-1)\ &=9 + 28\ &=37 \end{align*} ]

Step3: Apply quadratic formula

The quadratic formula is (x=\frac{-b\pm\sqrt{\Delta}}{2a}). Substitute (a = 7), (b = 3), (\Delta = 37) into the formula: [ \begin{align*} x&=\frac{-3\pm\sqrt{37}}{2\times7}\ &=\frac{-3\pm\sqrt{37}}{14} \end{align*} ]

Answer:

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