-x^2+5x+10=0

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Solution for -x^2+5x+10=0 equation: 


Simplifying
-1x2 + 5x + 10 = 0

Reorder the terms:
10 + 5x + -1x2 = 0

Solving
10 + 5x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + -5x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -5x + x2 = 0 + 10
-5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-5x + x2 = 10

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 = 10 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 10 + 6.25

Combine like terms: 10 + 6.25 = 16.25
6.25 + -5x + x2 = 16.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
x + -2.5 = 4.031128874

Simplifying
x + -2.5 = 4.031128874

Reorder the terms:
-2.5 + x = 4.031128874

Solving
-2.5 + x = 4.031128874

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 = 4.031128874 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.031128874 + 2.5
x = 4.031128874 + 2.5

Combine like terms: 4.031128874 + 2.5 = 6.531128874
x = 6.531128874

Simplifying
x = 6.531128874


Subproblem 2
x + -2.5 = -4.031128874

Simplifying
x + -2.5 = -4.031128874

Reorder the terms:
-2.5 + x = -4.031128874

Solving
-2.5 + x = -4.031128874

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 = -4.031128874 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.031128874 + 2.5
x = -4.031128874 + 2.5

Combine like terms: -4.031128874 + 2.5 = -1.531128874
x = -1.531128874

Simplifying
x = -1.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.531128874, -1.531128874}

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