x^2+4x=8

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Solution for x^2+4x=8 equation:


Simplifying
x2 + 4x = 8

Reorder the terms:
4x + x2 = 8

Solving
4x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 4x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 4x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 4x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 4x + x2 = 0 + 8
4x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
4x + x2 = 8

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 8 + 4

Reorder the terms:
4 + 4x + x2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + 4x + x2 = 12

Factor a perfect square on the left side:
(x + 2)(x + 2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 2) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + 2 = 3.464101615 Simplifying x + 2 = 3.464101615 Reorder the terms: 2 + x = 3.464101615 Solving 2 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.464101615 + -2 x = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 x = 1.464101615 Simplifying x = 1.464101615

Subproblem 2

x + 2 = -3.464101615 Simplifying x + 2 = -3.464101615 Reorder the terms: 2 + x = -3.464101615 Solving 2 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.464101615 + -2 x = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 x = -5.464101615 Simplifying x = -5.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.464101615, -5.464101615}

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