Question

solve.
$x^2 + 5x - 2 = 0$
enter your answers, as exact values, in the boxes.
$x = \square$ or $x = \square$

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=1$, $b=5$, $c=-2$

Step2: Apply quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Substitute coefficients

$x=\frac{-5\pm\sqrt{5^2-4(1)(-2)}}{2(1)}$

Step4: Simplify discriminant

$\sqrt{25+8}=\sqrt{33}$

Step5: Write final solutions

$x=\frac{-5+\sqrt{33}}{2}$ or $x=\frac{-5-\sqrt{33}}{2}$

Answer:

$x=\frac{-5+\sqrt{33}}{2}$ or $x=\frac{-5-\sqrt{33}}{2}$