Question

solve the following quadratic equation using the quadratic formula (5x^{2}+20x - 40 = 0)
use the keypad to enter the answer as a single simplified expression in the box. additional symbols can be found using the drop - down arrows at the top of the keypad.

the solutions or (x) values are (x=square) and (x = square).

Explanation:

Step1: Identify coefficients

For $5x^2 + 20x - 40 = 0$, we have $a=5$, $b=20$, $c=-40$.

Step2: Recall quadratic formula

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Step3: Calculate discriminant

$$\begin{align*} b^2 - 4ac &= 20^2 - 4(5)(-40)\\ &= 400 + 800\\ &= 1200 \end{align*}$$

Step4: Simplify square root

$\sqrt{1200} = \sqrt{100 \times 12} = 10\sqrt{12} = 10\sqrt{4 \times 3} = 20\sqrt{3}$

Step5: Substitute into formula

$$\begin{align*} x &= \frac{-20 \pm 20\sqrt{3}}{2(5)}\\ &= \frac{-20 \pm 20\sqrt{3}}{10} \end{align*}$$

Step6: Simplify the expression

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

Answer:

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