x^2-60x+90=0

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Solution for x^2-60x+90=0 equation:


Simplifying
x2 + -60x + 90 = 0

Reorder the terms:
90 + -60x + x2 = 0

Solving
90 + -60x + 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 + -60x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + -60x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -60x + x2 = 0 + -90
-60x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
-60x + x2 = -90

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = -90 + 900

Reorder the terms:
900 + -60x + x2 = -90 + 900

Combine like terms: -90 + 900 = 810
900 + -60x + x2 = 810

Factor a perfect square on the left side:
(x + -30)(x + -30) = 810

Calculate the square root of the right side: 28.460498942

Break this problem into two subproblems by setting 
(x + -30) equal to 28.460498942 and -28.460498942.

Subproblem 1

x + -30 = 28.460498942 Simplifying x + -30 = 28.460498942 Reorder the terms: -30 + x = 28.460498942 Solving -30 + x = 28.460498942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 28.460498942 + 30 Combine like terms: -30 + 30 = 0 0 + x = 28.460498942 + 30 x = 28.460498942 + 30 Combine like terms: 28.460498942 + 30 = 58.460498942 x = 58.460498942 Simplifying x = 58.460498942

Subproblem 2

x + -30 = -28.460498942 Simplifying x + -30 = -28.460498942 Reorder the terms: -30 + x = -28.460498942 Solving -30 + x = -28.460498942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -28.460498942 + 30 Combine like terms: -30 + 30 = 0 0 + x = -28.460498942 + 30 x = -28.460498942 + 30 Combine like terms: -28.460498942 + 30 = 1.539501058 x = 1.539501058 Simplifying x = 1.539501058

Solution

The solution to the problem is based on the solutions from the subproblems. x = {58.460498942, 1.539501058}

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