4x^2+16x+8=13

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Solution for 4x^2+16x+8=13 equation:


Simplifying
4x2 + 16x + 8 = 13

Reorder the terms:
8 + 16x + 4x2 = 13

Solving
8 + 16x + 4x2 = 13

Solving for variable 'x'.

Reorder the terms:
8 + -13 + 16x + 4x2 = 13 + -13

Combine like terms: 8 + -13 = -5
-5 + 16x + 4x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-5 + 16x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-1.25 + 4x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 4x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 4x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 4x + x2 = 0 + 1.25
4x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
4x + x2 = 1.25

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 = 1.25 + 4

Reorder the terms:
4 + 4x + x2 = 1.25 + 4

Combine like terms: 1.25 + 4 = 5.25
4 + 4x + x2 = 5.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 2) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + 2 = 2.291287847 Simplifying x + 2 = 2.291287847 Reorder the terms: 2 + x = 2.291287847 Solving 2 + x = 2.291287847 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 = 2.291287847 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.291287847 + -2 x = 2.291287847 + -2 Combine like terms: 2.291287847 + -2 = 0.291287847 x = 0.291287847 Simplifying x = 0.291287847

Subproblem 2

x + 2 = -2.291287847 Simplifying x + 2 = -2.291287847 Reorder the terms: 2 + x = -2.291287847 Solving 2 + x = -2.291287847 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 = -2.291287847 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.291287847 + -2 x = -2.291287847 + -2 Combine like terms: -2.291287847 + -2 = -4.291287847 x = -4.291287847 Simplifying x = -4.291287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.291287847, -4.291287847}

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