2x^2+10x+12=3136

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Solution for 2x^2+10x+12=3136 equation: 


Simplifying
2x2 + 10x + 12 = 3136

Reorder the terms:
12 + 10x + 2x2 = 3136

Solving
12 + 10x + 2x2 = 3136

Solving for variable 'x'.

Reorder the terms:
12 + -3136 + 10x + 2x2 = 3136 + -3136

Combine like terms: 12 + -3136 = -3124
-3124 + 10x + 2x2 = 3136 + -3136

Combine like terms: 3136 + -3136 = 0
-3124 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1562 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1562 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-1562 + 5x + x2 = 0

Solving
-1562 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1562' to each side of the equation.
-1562 + 5x + 1562 + x2 = 0 + 1562

Reorder the terms:
-1562 + 1562 + 5x + x2 = 0 + 1562

Combine like terms: -1562 + 1562 = 0
0 + 5x + x2 = 0 + 1562
5x + x2 = 0 + 1562

Combine like terms: 0 + 1562 = 1562
5x + x2 = 1562

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 1562 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1562 + 6.25

Combine like terms: 1562 + 6.25 = 1568.25
6.25 + 5x + x2 = 1568.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1568.25

Calculate the square root of the right side: 39.601136347

Break this problem into two subproblems by setting 
(x + 2.5) equal to 39.601136347 and -39.601136347.


Subproblem 1
x + 2.5 = 39.601136347

Simplifying
x + 2.5 = 39.601136347

Reorder the terms:
2.5 + x = 39.601136347

Solving
2.5 + x = 39.601136347

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 39.601136347 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 39.601136347 + -2.5
x = 39.601136347 + -2.5

Combine like terms: 39.601136347 + -2.5 = 37.101136347
x = 37.101136347

Simplifying
x = 37.101136347


Subproblem 2
x + 2.5 = -39.601136347

Simplifying
x + 2.5 = -39.601136347

Reorder the terms:
2.5 + x = -39.601136347

Solving
2.5 + x = -39.601136347

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -39.601136347 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -39.601136347 + -2.5
x = -39.601136347 + -2.5

Combine like terms: -39.601136347 + -2.5 = -42.101136347
x = -42.101136347

Simplifying
x = -42.101136347


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.101136347, -42.101136347}
Solution
x = {37.101136347, -42.101136347}

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