2x^2+10x-3=15

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Solution for 2x^2+10x-3=15 equation: 


Simplifying
2x2 + 10x + -3 = 15

Reorder the terms:
-3 + 10x + 2x2 = 15

Solving
-3 + 10x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
-3 + -15 + 10x + 2x2 = 15 + -15

Combine like terms: -3 + -15 = -18
-18 + 10x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-18 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 5x + x2 = 0

Solving
-9 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5x + x2 = 0 + 9
5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
5x + x2 = 9

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 = 9 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 9 + 6.25

Combine like terms: 9 + 6.25 = 15.25
6.25 + 5x + x2 = 15.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + 2.5 = 3.905124838

Simplifying
x + 2.5 = 3.905124838

Reorder the terms:
2.5 + x = 3.905124838

Solving
2.5 + x = 3.905124838

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 = 3.905124838 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.905124838 + -2.5
x = 3.905124838 + -2.5

Combine like terms: 3.905124838 + -2.5 = 1.405124838
x = 1.405124838

Simplifying
x = 1.405124838


Subproblem 2
x + 2.5 = -3.905124838

Simplifying
x + 2.5 = -3.905124838

Reorder the terms:
2.5 + x = -3.905124838

Solving
2.5 + x = -3.905124838

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 = -3.905124838 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.905124838 + -2.5
x = -3.905124838 + -2.5

Combine like terms: -3.905124838 + -2.5 = -6.405124838
x = -6.405124838

Simplifying
x = -6.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.405124838, -6.405124838}
Solution
x = {1.405124838, -6.405124838}

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