2x^2-10x=-10.5

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Solution for 2x^2-10x=-10.5 equation: 


Simplifying
2x2 + -10x = -10.5

Reorder the terms:
-10x + 2x2 = -10.5

Solving
-10x + 2x2 = -10.5

Solving for variable 'x'.

Reorder the terms:
10.5 + -10x + 2x2 = -10.5 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
10.5 + -10x + 2x2 = 0.0

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

Divide each side by '2'.
5.25 + -5x + x2 = 0.0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -5x + -5.25 + x2 = 0.0 + -5.25

Reorder the terms:
5.25 + -5.25 + -5x + x2 = 0.0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -5x + x2 = 0.0 + -5.25
-5x + x2 = 0.0 + -5.25

Combine like terms: 0.0 + -5.25 = -5.25
-5x + x2 = -5.25

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 = -5.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5.25 + 6.25

Combine like terms: -5.25 + 6.25 = 1
6.25 + -5x + x2 = 1

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1 and -1.


Subproblem 1
x + -2.5 = 1

Simplifying
x + -2.5 = 1

Reorder the terms:
-2.5 + x = 1

Solving
-2.5 + x = 1

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 = 1 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1 + 2.5
x = 1 + 2.5

Combine like terms: 1 + 2.5 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + -2.5 = -1

Simplifying
x + -2.5 = -1

Reorder the terms:
-2.5 + x = -1

Solving
-2.5 + x = -1

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 = -1 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1 + 2.5
x = -1 + 2.5

Combine like terms: -1 + 2.5 = 1.5
x = 1.5

Simplifying
x = 1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, 1.5}

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