Question

use the quadratic formula to solve the equation.
$x^2 + 3x - 5 = 0$
$x = \square$
(type an exact answer, using radicals as needed. use a con

Explanation:

Step1: Identify coefficients

For $ax^2+bx+c=0$, $a=1$, $b=3$, $c=-5$

Step2: Recall quadratic formula

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

Step3: Substitute values into formula

$x=\frac{-3\pm\sqrt{3^2-4(1)(-5)}}{2(1)}$

Step4: Simplify discriminant

$\sqrt{9+20}=\sqrt{29}$

Step5: Final simplification

$x=\frac{-3\pm\sqrt{29}}{2}$

Answer:

$x=\frac{-3+\sqrt{29}}{2}$ and $x=\frac{-3-\sqrt{29}}{2}$