x^2-10x+25=84

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Solution for x^2-10x+25=84 equation: 


Simplifying
x2 + -10x + 25 = 84

Reorder the terms:
25 + -10x + x2 = 84

Solving
25 + -10x + x2 = 84

Solving for variable 'x'.

Reorder the terms:
25 + -84 + -10x + x2 = 84 + -84

Combine like terms: 25 + -84 = -59
-59 + -10x + x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-59 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + -10x + 59 + x2 = 0 + 59

Reorder the terms:
-59 + 59 + -10x + x2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + -10x + x2 = 0 + 59
-10x + x2 = 0 + 59

Combine like terms: 0 + 59 = 59
-10x + x2 = 59

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 59 + 25

Reorder the terms:
25 + -10x + x2 = 59 + 25

Combine like terms: 59 + 25 = 84
25 + -10x + x2 = 84

Factor a perfect square on the left side:
(x + -5)(x + -5) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + -5) equal to 9.16515139 and -9.16515139.


Subproblem 1
x + -5 = 9.16515139

Simplifying
x + -5 = 9.16515139

Reorder the terms:
-5 + x = 9.16515139

Solving
-5 + x = 9.16515139

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x = 9.16515139 + 5

Combine like terms: -5 + 5 = 0
0 + x = 9.16515139 + 5
x = 9.16515139 + 5

Combine like terms: 9.16515139 + 5 = 14.16515139
x = 14.16515139

Simplifying
x = 14.16515139


Subproblem 2
x + -5 = -9.16515139

Simplifying
x + -5 = -9.16515139

Reorder the terms:
-5 + x = -9.16515139

Solving
-5 + x = -9.16515139

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x = -9.16515139 + 5

Combine like terms: -5 + 5 = 0
0 + x = -9.16515139 + 5
x = -9.16515139 + 5

Combine like terms: -9.16515139 + 5 = -4.16515139
x = -4.16515139

Simplifying
x = -4.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.16515139, -4.16515139}

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