x^2-20x-90.25=

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Solution for x^2-20x-90.25= equation:


Simplifying
x2 + -20x + -90.25 = 0

Reorder the terms:
-90.25 + -20x + x2 = 0

Solving
-90.25 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '90.25' to each side of the equation.
-90.25 + -20x + 90.25 + x2 = 0 + 90.25

Reorder the terms:
-90.25 + 90.25 + -20x + x2 = 0 + 90.25

Combine like terms: -90.25 + 90.25 = 0.00
0.00 + -20x + x2 = 0 + 90.25
-20x + x2 = 0 + 90.25

Combine like terms: 0 + 90.25 = 90.25
-20x + x2 = 90.25

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 = 90.25 + 100

Reorder the terms:
100 + -20x + x2 = 90.25 + 100

Combine like terms: 90.25 + 100 = 190.25
100 + -20x + x2 = 190.25

Factor a perfect square on the left side:
(x + -10)(x + -10) = 190.25

Calculate the square root of the right side: 13.793114224

Break this problem into two subproblems by setting 
(x + -10) equal to 13.793114224 and -13.793114224.

Subproblem 1

x + -10 = 13.793114224 Simplifying x + -10 = 13.793114224 Reorder the terms: -10 + x = 13.793114224 Solving -10 + x = 13.793114224 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 = 13.793114224 + 10 Combine like terms: -10 + 10 = 0 0 + x = 13.793114224 + 10 x = 13.793114224 + 10 Combine like terms: 13.793114224 + 10 = 23.793114224 x = 23.793114224 Simplifying x = 23.793114224

Subproblem 2

x + -10 = -13.793114224 Simplifying x + -10 = -13.793114224 Reorder the terms: -10 + x = -13.793114224 Solving -10 + x = -13.793114224 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 = -13.793114224 + 10 Combine like terms: -10 + 10 = 0 0 + x = -13.793114224 + 10 x = -13.793114224 + 10 Combine like terms: -13.793114224 + 10 = -3.793114224 x = -3.793114224 Simplifying x = -3.793114224

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.793114224, -3.793114224}

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