How do you solve #x^2 + 8x = 24# using the quadratic formula?

Question

Hazel Anglin · Accepted Answer

#x = - 4 pm 2 sqrt(10)#

We have: #x^(2) + 8 x = 24#

First, let's subtract #24# from both sides of the equation:

#=> x^(2) + 8 x - 24 = 0#

Next, let's use the formula for quadratics:

#=> x = (- 8 pm sqrt(8^(2) - 4 (1) (- 24))) / (2 (1))#

#=> x = (- 8 pm sqrt(64 + 96)) / (2)#

#=> x = (- 8 pm sqrt(160)) / (2)#

#=> x = (- 8 pm 4 sqrt(10)) / (2)#

#=> x = - 4 pm 2 sqrt(10)#

Therefore, the solutions to the equation are #x = - 4 - 2 sqrt(10)# and #x = - 4 + 2 sqrt(10)#.

Jace Anderson · Answer

undefined To solve the equation $x^2 + 8x = 24$ using the quadratic formula, follow these steps:

1. Rewrite the equation in the form $ax^2 + bx + c = 0$. In this case, $a = 1$, $b = 8$, and $c = -24$.

2. Substitute the values of $a$, $b$, and $c$ into the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$.

3. Plug in the values: $x = \frac{{-8 \pm \sqrt{{8^2 - 4 \cdot 1 \cdot (-24)}}}}{{2 \cdot 1}}$.

4. Simplify: $x = \frac{{-8 \pm \sqrt{{64 + 96}}}}{2}$.

5. Further simplify: $x = \frac{{-8 \pm \sqrt{{160}}}}{2}$.

6. Simplify the square root: $x = \frac{{-8 \pm 4\sqrt{{10}}}}{2}$.

7. Simplify the expression: $x = -4 \pm 2\sqrt{10}$.

Therefore, the solutions to the equation $x^2 + 8x = 24$ are $x = -4 + 2\sqrt{10}$ and $x = -4 - 2\sqrt{10}$.