2x^2+10x-298=0

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Solution for 2x^2+10x-298=0 equation: 


Simplifying
2x2 + 10x + -298 = 0

Reorder the terms:
-298 + 10x + 2x2 = 0

Solving
-298 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-149 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-149 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-149 + 5x + x2 = 0

Solving
-149 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '149' to each side of the equation.
-149 + 5x + 149 + x2 = 0 + 149

Reorder the terms:
-149 + 149 + 5x + x2 = 0 + 149

Combine like terms: -149 + 149 = 0
0 + 5x + x2 = 0 + 149
5x + x2 = 0 + 149

Combine like terms: 0 + 149 = 149
5x + x2 = 149

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 = 149 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 149 + 6.25

Combine like terms: 149 + 6.25 = 155.25
6.25 + 5x + x2 = 155.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 155.25

Calculate the square root of the right side: 12.459935794

Break this problem into two subproblems by setting 
(x + 2.5) equal to 12.459935794 and -12.459935794.


Subproblem 1
x + 2.5 = 12.459935794

Simplifying
x + 2.5 = 12.459935794

Reorder the terms:
2.5 + x = 12.459935794

Solving
2.5 + x = 12.459935794

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 = 12.459935794 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 12.459935794 + -2.5
x = 12.459935794 + -2.5

Combine like terms: 12.459935794 + -2.5 = 9.959935794
x = 9.959935794

Simplifying
x = 9.959935794


Subproblem 2
x + 2.5 = -12.459935794

Simplifying
x + 2.5 = -12.459935794

Reorder the terms:
2.5 + x = -12.459935794

Solving
2.5 + x = -12.459935794

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 = -12.459935794 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -12.459935794 + -2.5
x = -12.459935794 + -2.5

Combine like terms: -12.459935794 + -2.5 = -14.959935794
x = -14.959935794

Simplifying
x = -14.959935794


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.959935794, -14.959935794}
Solution
x = {9.959935794, -14.959935794}

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