2x^2-10x-28=8

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Solution for 2x^2-10x-28=8 equation: 


Simplifying
2x2 + -10x + -28 = 8

Reorder the terms:
-28 + -10x + 2x2 = 8

Solving
-28 + -10x + 2x2 = 8

Solving for variable 'x'.

Reorder the terms:
-28 + -8 + -10x + 2x2 = 8 + -8

Combine like terms: -28 + -8 = -36
-36 + -10x + 2x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-36 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-18 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-18 + -5x + x2 = 0

Solving
-18 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -5x + x2 = 0 + 18
-5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-5x + x2 = 18

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 = 18 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + -5x + x2 = 24.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + -2.5 = 4.924428901

Simplifying
x + -2.5 = 4.924428901

Reorder the terms:
-2.5 + x = 4.924428901

Solving
-2.5 + x = 4.924428901

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 = 4.924428901 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.924428901 + 2.5
x = 4.924428901 + 2.5

Combine like terms: 4.924428901 + 2.5 = 7.424428901
x = 7.424428901

Simplifying
x = 7.424428901


Subproblem 2
x + -2.5 = -4.924428901

Simplifying
x + -2.5 = -4.924428901

Reorder the terms:
-2.5 + x = -4.924428901

Solving
-2.5 + x = -4.924428901

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 = -4.924428901 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.924428901 + 2.5
x = -4.924428901 + 2.5

Combine like terms: -4.924428901 + 2.5 = -2.424428901
x = -2.424428901

Simplifying
x = -2.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.424428901, -2.424428901}
Solution
x = {7.424428901, -2.424428901}

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