10x^2-16=-14x^2+10x+50

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Solution for 10x^2-16=-14x^2+10x+50 equation: 


Simplifying
10x2 + -16 = -14x2 + 10x + 50

Reorder the terms:
-16 + 10x2 = -14x2 + 10x + 50

Reorder the terms:
-16 + 10x2 = 50 + 10x + -14x2

Solving
-16 + 10x2 = 50 + 10x + -14x2

Solving for variable 'x'.

Reorder the terms:
-16 + -50 + -10x + 10x2 + 14x2 = 50 + 10x + -14x2 + -50 + -10x + 14x2

Combine like terms: -16 + -50 = -66
-66 + -10x + 10x2 + 14x2 = 50 + 10x + -14x2 + -50 + -10x + 14x2

Combine like terms: 10x2 + 14x2 = 24x2
-66 + -10x + 24x2 = 50 + 10x + -14x2 + -50 + -10x + 14x2

Reorder the terms:
-66 + -10x + 24x2 = 50 + -50 + 10x + -10x + -14x2 + 14x2

Combine like terms: 50 + -50 = 0
-66 + -10x + 24x2 = 0 + 10x + -10x + -14x2 + 14x2
-66 + -10x + 24x2 = 10x + -10x + -14x2 + 14x2

Combine like terms: 10x + -10x = 0
-66 + -10x + 24x2 = 0 + -14x2 + 14x2
-66 + -10x + 24x2 = -14x2 + 14x2

Combine like terms: -14x2 + 14x2 = 0
-66 + -10x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -5x + 12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-33 + -5x + 12x2)' equal to zero and attempt to solve:

Simplifying
-33 + -5x + 12x2 = 0

Solving
-33 + -5x + 12x2 = 0

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

Divide each side by '12'.
-2.75 + -0.4166666667x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -0.4166666667x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -0.4166666667x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -0.4166666667x + x2 = 0 + 2.75
-0.4166666667x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-0.4166666667x + x2 = 2.75

The x term is -0.4166666667x.  Take half its coefficient (-0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
-0.4166666667x + 0.04340277781 + x2 = 2.75 + 0.04340277781

Reorder the terms:
0.04340277781 + -0.4166666667x + x2 = 2.75 + 0.04340277781

Combine like terms: 2.75 + 0.04340277781 = 2.79340277781
0.04340277781 + -0.4166666667x + x2 = 2.79340277781

Factor a perfect square on the left side:
(x + -0.2083333334)(x + -0.2083333334) = 2.79340277781

Calculate the square root of the right side: 1.671347593

Break this problem into two subproblems by setting 
(x + -0.2083333334) equal to 1.671347593 and -1.671347593.


Subproblem 1
x + -0.2083333334 = 1.671347593

Simplifying
x + -0.2083333334 = 1.671347593

Reorder the terms:
-0.2083333334 + x = 1.671347593

Solving
-0.2083333334 + x = 1.671347593

Solving for variable 'x'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x = 1.671347593 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x = 1.671347593 + 0.2083333334
x = 1.671347593 + 0.2083333334

Combine like terms: 1.671347593 + 0.2083333334 = 1.8796809264
x = 1.8796809264

Simplifying
x = 1.8796809264


Subproblem 2
x + -0.2083333334 = -1.671347593

Simplifying
x + -0.2083333334 = -1.671347593

Reorder the terms:
-0.2083333334 + x = -1.671347593

Solving
-0.2083333334 + x = -1.671347593

Solving for variable 'x'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x = -1.671347593 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x = -1.671347593 + 0.2083333334
x = -1.671347593 + 0.2083333334

Combine like terms: -1.671347593 + 0.2083333334 = -1.4630142596
x = -1.4630142596

Simplifying
x = -1.4630142596


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8796809264, -1.4630142596}
Solution
x = {1.8796809264, -1.4630142596}

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