How do you solve using the quadratic formula #x^2-7x-8=0#?

Question

Eva Adamson · Accepted Answer

#x = 8# and #x = -1#

This quadratic can be factored to:

#(x - 8)(x + 1) = 0#

Solving for #(x - 8)# gives:

#((x - 8)(x + 1))/((x + 1)) = 0/(x + 1)#

#x - 8 = 0#

#x - 8 + 8 = 0 + 8#

#x = 8#

Solving for #(x + 1)# gives:

#((x - 8)(x + 1))/((x - 8)) = 0/(x - 8)#

#x + 1 = 0#

#x + 1 - 1 = 0 - 1#

#x = -1#

Hazel Anglin · Answer

undefined To solve the quadratic equation $x^2 - 7x - 8 = 0$, you can use the quadratic formula, which is given by:

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

where $a$, $b$, and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$.

For the equation $x^2 - 7x - 8 = 0$:
- $a = 1$
- $b = -7$
- $c = -8$

Plugging these values into the quadratic formula:

$$x = \frac{{-(-7) \pm \sqrt{{(-7)^2 - 4(1)(-8)}}}}{{2(1)}}$$

Simplify inside the square root:

$$x = \frac{{7 \pm \sqrt{{49 + 32}}}}{2}$$

$$x = \frac{{7 \pm \sqrt{81}}}{2}$$

$$x = \frac{{7 \pm 9}}{2}$$

This gives two possible solutions:

$$x_1 = \frac{{7 + 9}}{2} = 8$$
$$x_2 = \frac{{7 - 9}}{2} = -1$$

Therefore, the solutions to the equation $x^2 - 7x - 8 = 0$ are $x = 8$ and $x = -1$.