# How do you solve x^2+8x+7=0?

Aug 15, 2015

The solutions are
color(blue)(x=-7,x=-1

#### Explanation:

${x}^{2} + 8 x + 7 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 8 , c = 7$

The Discriminant is given by:

color(blue)(Delta=b^2-4*a*c
$= {\left(8\right)}^{2} - \left(4 \cdot 1 \cdot 7\right)$
$= 64 - 28 = 36$

The solutions are found using the formula
color(blue)(x=(-b+-sqrtDelta)/(2*a)

$x = \frac{\left(- 8\right) \pm \sqrt{36}}{2 \cdot 1} = \frac{\left(- 8 \pm 6\right)}{2}$

x=(-8-6)/2, color(blue)(x=-7

x=(-8+6)/2, color(blue)(x=-1

Aug 16, 2015

Solve y = x^2 + 8x + 7 = 0

Ans: -1 and -7

#### Explanation:

Since (a - b + c = 0), use the shortcut. The 2 real roots are (- 1) and (-c/a = - 7).

Reminder of Shortcut :
a. When a + b + c = 0: 2 real roots: (1) and (c/a)
b. When (a - b + c ) = 0: 2 real roots: (-1) and (-c/a)
Remember this Shortcut. It will save you a lot of time and effort.