solve the quadratic equation.\n2x² + 5x - 8 = 0\nwrite one exact solution in each box. you can add or remove…

Explanation:

Step1: Identify coefficients

For the quadratic equation $2x^{2}+5x - 8=0$, we have $a = 2$, $b = 5$, $c=-8$.

Step2: Write quadratic formula

The quadratic formula for a quadratic equation $ax^{2}+bx + c = 0$ is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Calculate discriminant

First, calculate the discriminant $\Delta=b^{2}-4ac$. Substitute $a = 2$, $b = 5$, $c=-8$ into it: $\Delta=5^{2}-4\times2\times(-8)=25 + 64=89$.

Step4: Find solutions

Substitute $a = 2$, $b = 5$, $\Delta = 89$ into the quadratic formula: $x=\frac{-5\pm\sqrt{89}}{2\times2}=\frac{-5\pm\sqrt{89}}{4}$.

Answer:

$x=\frac{-5 + \sqrt{89}}{4}$, $x=\frac{-5-\sqrt{89}}{4}$