x^2-8x+10=180

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Solution for x^2-8x+10=180 equation:


Simplifying
x2 + -8x + 10 = 180

Reorder the terms:
10 + -8x + x2 = 180

Solving
10 + -8x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
10 + -180 + -8x + x2 = 180 + -180

Combine like terms: 10 + -180 = -170
-170 + -8x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-170 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '170' to each side of the equation.
-170 + -8x + 170 + x2 = 0 + 170

Reorder the terms:
-170 + 170 + -8x + x2 = 0 + 170

Combine like terms: -170 + 170 = 0
0 + -8x + x2 = 0 + 170
-8x + x2 = 0 + 170

Combine like terms: 0 + 170 = 170
-8x + x2 = 170

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 170 + 16

Reorder the terms:
16 + -8x + x2 = 170 + 16

Combine like terms: 170 + 16 = 186
16 + -8x + x2 = 186

Factor a perfect square on the left side:
(x + -4)(x + -4) = 186

Calculate the square root of the right side: 13.638181697

Break this problem into two subproblems by setting 
(x + -4) equal to 13.638181697 and -13.638181697.

Subproblem 1

x + -4 = 13.638181697 Simplifying x + -4 = 13.638181697 Reorder the terms: -4 + x = 13.638181697 Solving -4 + x = 13.638181697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 13.638181697 + 4 Combine like terms: -4 + 4 = 0 0 + x = 13.638181697 + 4 x = 13.638181697 + 4 Combine like terms: 13.638181697 + 4 = 17.638181697 x = 17.638181697 Simplifying x = 17.638181697

Subproblem 2

x + -4 = -13.638181697 Simplifying x + -4 = -13.638181697 Reorder the terms: -4 + x = -13.638181697 Solving -4 + x = -13.638181697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -13.638181697 + 4 Combine like terms: -4 + 4 = 0 0 + x = -13.638181697 + 4 x = -13.638181697 + 4 Combine like terms: -13.638181697 + 4 = -9.638181697 x = -9.638181697 Simplifying x = -9.638181697

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.638181697, -9.638181697}

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