Question

What are the solutions to the equation? x2 + 6x = 40

Answer 1

`x_1= 4\\x_2=-10`

Explanation:

`x^2+6x=40`

Since it is an equation squared to find the two values of x we can apply the formula of the solver

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

we equate the equation to zero to be able to apply the solver

`x^2+6x=40\\x^2+6x-40=0`

`a=1 \\b=6\\c=-40`

`x = \frac {-6 \pm \sqrt {(6)^2 - 4(1)(-40)}}{2(1)}\\x = \frac {-6 \pm \sqrt {36+160}}{2}\\x = \frac {-6 \pm \sqrt {196}}{2}\\x = \frac {-6 \pm \ 14}{2}\\x_1=  \frac {-6 +\ 14}{2}\\x_1= (8)/(2)= 4\\x_2=\frac {-6 - 14}{2}\\x_2=(-20)/(2)= -10`

`x_1= 4\\x_2=-10`

Answer 2

x² + 6x = 40

Subtract 40 from both sides:

x² + 6x - 40 = 40 - 40

refine: x² + 6x - 40 = 0

factor x² + 6x - 40 = 0

( x- 4 ) ( x + 10 ) = 0

solve x - 4 = 0

x = 0 + 4

x = 4

solve x + 10 = 0

x = 0 - 10

x = - 10

solution : x = 4 , x = - 10

hope this helps!