solve the quadratic equation.\n-7x² + x + 1 = 0\nwrite one exact solution in each box. you can add or remove…

Explanation:

Step1: Identify coefficients

For the quadratic equation $-7x^{2}+x + 1=0$, we have $a=-7$, $b = 1$, $c = 1$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(1)^{2}-4\times(-7)\times1=1 + 28=29$.

Step3: Use the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substitute $a=-7$, $b = 1$, $\Delta = 29$: $x=\frac{-1\pm\sqrt{29}}{2\times(-7)}=\frac{-1\pm\sqrt{29}}{-14}=\frac{1\pm\sqrt{29}}{14}$.

Answer:

$x=\frac{1+\sqrt{29}}{14}$, $x=\frac{1 - \sqrt{29}}{14}$