x^2-(5x+60)-10=0

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Solution for x^2-(5x+60)-10=0 equation: 


Simplifying
x2 + -1(5x + 60) + -10 = 0

Reorder the terms:
x2 + -1(60 + 5x) + -10 = 0
x2 + (60 * -1 + 5x * -1) + -10 = 0
x2 + (-60 + -5x) + -10 = 0

Reorder the terms:
-60 + -10 + -5x + x2 = 0

Combine like terms: -60 + -10 = -70
-70 + -5x + x2 = 0

Solving
-70 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + -5x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + -5x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -5x + x2 = 0 + 70
-5x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
-5x + x2 = 70

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 = 70 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 70 + 6.25

Combine like terms: 70 + 6.25 = 76.25
6.25 + -5x + x2 = 76.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(x + -2.5) equal to 8.732124598 and -8.732124598.


Subproblem 1
x + -2.5 = 8.732124598

Simplifying
x + -2.5 = 8.732124598

Reorder the terms:
-2.5 + x = 8.732124598

Solving
-2.5 + x = 8.732124598

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 = 8.732124598 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 8.732124598 + 2.5
x = 8.732124598 + 2.5

Combine like terms: 8.732124598 + 2.5 = 11.232124598
x = 11.232124598

Simplifying
x = 11.232124598


Subproblem 2
x + -2.5 = -8.732124598

Simplifying
x + -2.5 = -8.732124598

Reorder the terms:
-2.5 + x = -8.732124598

Solving
-2.5 + x = -8.732124598

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 = -8.732124598 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -8.732124598 + 2.5
x = -8.732124598 + 2.5

Combine like terms: -8.732124598 + 2.5 = -6.232124598
x = -6.232124598

Simplifying
x = -6.232124598


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.232124598, -6.232124598}

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