x^2+8x+16=40

Simple and best practice solution for x^2+8x+16=40 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2+8x+16=40 equation: 


Simplifying
x2 + 8x + 16 = 40

Reorder the terms:
16 + 8x + x2 = 40

Solving
16 + 8x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
16 + -40 + 8x + x2 = 40 + -40

Combine like terms: 16 + -40 = -24
-24 + 8x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-24 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 8x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 8x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 8x + x2 = 0 + 24
8x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
8x + x2 = 24

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 24 + 16

Reorder the terms:
16 + 8x + x2 = 24 + 16

Combine like terms: 24 + 16 = 40
16 + 8x + x2 = 40

Factor a perfect square on the left side:
(x + 4)(x + 4) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 4) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + 4 = 6.32455532

Simplifying
x + 4 = 6.32455532

Reorder the terms:
4 + x = 6.32455532

Solving
4 + x = 6.32455532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 6.32455532 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.32455532 + -4
x = 6.32455532 + -4

Combine like terms: 6.32455532 + -4 = 2.32455532
x = 2.32455532

Simplifying
x = 2.32455532


Subproblem 2
x + 4 = -6.32455532

Simplifying
x + 4 = -6.32455532

Reorder the terms:
4 + x = -6.32455532

Solving
4 + x = -6.32455532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = -6.32455532 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.32455532 + -4
x = -6.32455532 + -4

Combine like terms: -6.32455532 + -4 = -10.32455532
x = -10.32455532

Simplifying
x = -10.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.32455532, -10.32455532}

See similar equations:

| 20=3z+5 | | 157k-19c= | | 3a-1+4a=92 | | 30=p-8+8 | | 2(x+3)=2+6 | | 83+x=129 | | 10x1/5x | | 4+4u=12 | | 5-3x=-14-3x | | 9x+10=12x-14 | | 5(6x+10)=-20 | | -16=-8+n | | 11n-15-10n-14=4 | | 83-x=129 | | 2+3a=32 | | 8x+8b=5b-2x | | 12+x=2001 | | -3x=4y-6 | | p^5q^9/(pq)^3 | | 2x+41=99 | | -a+4=20 | | 8-9r=-19 | | 4x=4+2 | | -6=-2(-4+m) | | 8-7u=-13 | | 105+3x+2x=180 | | w+6=12 | | 22=2-4b | | 6-4h=9 | | 4z-5=11z+5 | | g-32.5=7.5g | | 2y-(-112)=-24 |

Equations solver categories