150=2x^2+4x-6

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Solution for 150=2x^2+4x-6 equation: 


Simplifying
150 = 2x2 + 4x + -6

Reorder the terms:
150 = -6 + 4x + 2x2

Solving
150 = -6 + 4x + 2x2

Solving for variable 'x'.

Combine like terms: 150 + 6 = 156
156 + -4x + -2x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2

Reorder the terms:
156 + -4x + -2x2 = -6 + 6 + 4x + -4x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
156 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
156 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
156 + -4x + -2x2 = 0 + 2x2 + -2x2
156 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
156 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(78 + -2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(78 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
78 + -2x + -1x2 = 0

Solving
78 + -2x + -1x2 = 0

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

Divide each side by '-1'.
-78 + 2x + x2 = 0

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 2x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + 2x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 2x + x2 = 0 + 78
2x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
2x + x2 = 78

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 78 + 1

Reorder the terms:
1 + 2x + x2 = 78 + 1

Combine like terms: 78 + 1 = 79
1 + 2x + x2 = 79

Factor a perfect square on the left side:
(x + 1)(x + 1) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + 1) equal to 8.888194417 and -8.888194417.


Subproblem 1
x + 1 = 8.888194417

Simplifying
x + 1 = 8.888194417

Reorder the terms:
1 + x = 8.888194417

Solving
1 + x = 8.888194417

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 8.888194417 + -1

Combine like terms: 1 + -1 = 0
0 + x = 8.888194417 + -1
x = 8.888194417 + -1

Combine like terms: 8.888194417 + -1 = 7.888194417
x = 7.888194417

Simplifying
x = 7.888194417


Subproblem 2
x + 1 = -8.888194417

Simplifying
x + 1 = -8.888194417

Reorder the terms:
1 + x = -8.888194417

Solving
1 + x = -8.888194417

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -8.888194417 + -1

Combine like terms: 1 + -1 = 0
0 + x = -8.888194417 + -1
x = -8.888194417 + -1

Combine like terms: -8.888194417 + -1 = -9.888194417
x = -9.888194417

Simplifying
x = -9.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.888194417, -9.888194417}
Solution
x = {7.888194417, -9.888194417}

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