x^2+8x+16=28

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Solution for x^2+8x+16=28 equation:


Simplifying
x2 + 8x + 16 = 28

Reorder the terms:
16 + 8x + x2 = 28

Solving
16 + 8x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
16 + -28 + 8x + x2 = 28 + -28

Combine like terms: 16 + -28 = -12
-12 + 8x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-12 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 8x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 8x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 8x + x2 = 0 + 12
8x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
8x + x2 = 12

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 = 12 + 16

Reorder the terms:
16 + 8x + x2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + 8x + x2 = 28

Factor a perfect square on the left side:
(x + 4)(x + 4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + 4) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + 4 = 5.291502622 Simplifying x + 4 = 5.291502622 Reorder the terms: 4 + x = 5.291502622 Solving 4 + x = 5.291502622 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 = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.291502622 + -4 x = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 x = 1.291502622 Simplifying x = 1.291502622

Subproblem 2

x + 4 = -5.291502622 Simplifying x + 4 = -5.291502622 Reorder the terms: 4 + x = -5.291502622 Solving 4 + x = -5.291502622 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 = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.291502622 + -4 x = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 x = -9.291502622 Simplifying x = -9.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.291502622, -9.291502622}

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