472=4x^2+16x

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Solution for 472=4x^2+16x equation: 


Simplifying
472 = 4x2 + 16x

Reorder the terms:
472 = 16x + 4x2

Solving
472 = 16x + 4x2

Solving for variable 'x'.

Reorder the terms:
472 + -16x + -4x2 = 16x + -16x + 4x2 + -4x2

Combine like terms: 16x + -16x = 0
472 + -16x + -4x2 = 0 + 4x2 + -4x2
472 + -16x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
472 + -16x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(118 + -4x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(118 + -4x + -1x2)' equal to zero and attempt to solve:

Simplifying
118 + -4x + -1x2 = 0

Solving
118 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-118 + 4x + x2 = 0

Move the constant term to the right:

Add '118' to each side of the equation.
-118 + 4x + 118 + x2 = 0 + 118

Reorder the terms:
-118 + 118 + 4x + x2 = 0 + 118

Combine like terms: -118 + 118 = 0
0 + 4x + x2 = 0 + 118
4x + x2 = 0 + 118

Combine like terms: 0 + 118 = 118
4x + x2 = 118

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 = 118 + 4

Reorder the terms:
4 + 4x + x2 = 118 + 4

Combine like terms: 118 + 4 = 122
4 + 4x + x2 = 122

Factor a perfect square on the left side:
(x + 2)(x + 2) = 122

Calculate the square root of the right side: 11.045361017

Break this problem into two subproblems by setting 
(x + 2) equal to 11.045361017 and -11.045361017.


Subproblem 1
x + 2 = 11.045361017

Simplifying
x + 2 = 11.045361017

Reorder the terms:
2 + x = 11.045361017

Solving
2 + x = 11.045361017

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 = 11.045361017 + -2

Combine like terms: 2 + -2 = 0
0 + x = 11.045361017 + -2
x = 11.045361017 + -2

Combine like terms: 11.045361017 + -2 = 9.045361017
x = 9.045361017

Simplifying
x = 9.045361017


Subproblem 2
x + 2 = -11.045361017

Simplifying
x + 2 = -11.045361017

Reorder the terms:
2 + x = -11.045361017

Solving
2 + x = -11.045361017

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 = -11.045361017 + -2

Combine like terms: 2 + -2 = 0
0 + x = -11.045361017 + -2
x = -11.045361017 + -2

Combine like terms: -11.045361017 + -2 = -13.045361017
x = -13.045361017

Simplifying
x = -13.045361017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.045361017, -13.045361017}
Solution
x = {9.045361017, -13.045361017}

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