x^2-20x+90=0

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Solution for x^2-20x+90=0 equation:


Simplifying
x2 + -20x + 90 = 0

Reorder the terms:
90 + -20x + x2 = 0

Solving
90 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + -20x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + -20x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -20x + x2 = 0 + -90
-20x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
-20x + x2 = -90

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -90 + 100

Reorder the terms:
100 + -20x + x2 = -90 + 100

Combine like terms: -90 + 100 = 10
100 + -20x + x2 = 10

Factor a perfect square on the left side:
(x + -10)(x + -10) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -10) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + -10 = 3.16227766 Simplifying x + -10 = 3.16227766 Reorder the terms: -10 + x = 3.16227766 Solving -10 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 3.16227766 + 10 Combine like terms: -10 + 10 = 0 0 + x = 3.16227766 + 10 x = 3.16227766 + 10 Combine like terms: 3.16227766 + 10 = 13.16227766 x = 13.16227766 Simplifying x = 13.16227766

Subproblem 2

x + -10 = -3.16227766 Simplifying x + -10 = -3.16227766 Reorder the terms: -10 + x = -3.16227766 Solving -10 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -3.16227766 + 10 Combine like terms: -10 + 10 = 0 0 + x = -3.16227766 + 10 x = -3.16227766 + 10 Combine like terms: -3.16227766 + 10 = 6.83772234 x = 6.83772234 Simplifying x = 6.83772234

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.16227766, 6.83772234}

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