-x^2+4x+14=4x^2

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Solution for -x^2+4x+14=4x^2 equation: 


Simplifying
-1x2 + 4x + 14 = 4x2

Reorder the terms:
14 + 4x + -1x2 = 4x2

Solving
14 + 4x + -1x2 = 4x2

Solving for variable 'x'.

Combine like terms: -1x2 + -4x2 = -5x2
14 + 4x + -5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
14 + 4x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.8 + -0.8x + x2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -0.8x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -0.8x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -0.8x + x2 = 0 + 2.8
-0.8x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-0.8x + x2 = 2.8

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 2.8 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 2.8 + 0.16

Combine like terms: 2.8 + 0.16 = 2.96
0.16 + -0.8x + x2 = 2.96

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 2.96

Calculate the square root of the right side: 1.720465053

Break this problem into two subproblems by setting 
(x + -0.4) equal to 1.720465053 and -1.720465053.


Subproblem 1
x + -0.4 = 1.720465053

Simplifying
x + -0.4 = 1.720465053

Reorder the terms:
-0.4 + x = 1.720465053

Solving
-0.4 + x = 1.720465053

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 1.720465053 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 1.720465053 + 0.4
x = 1.720465053 + 0.4

Combine like terms: 1.720465053 + 0.4 = 2.120465053
x = 2.120465053

Simplifying
x = 2.120465053


Subproblem 2
x + -0.4 = -1.720465053

Simplifying
x + -0.4 = -1.720465053

Reorder the terms:
-0.4 + x = -1.720465053

Solving
-0.4 + x = -1.720465053

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -1.720465053 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -1.720465053 + 0.4
x = -1.720465053 + 0.4

Combine like terms: -1.720465053 + 0.4 = -1.320465053
x = -1.320465053

Simplifying
x = -1.320465053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.120465053, -1.320465053}

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