x^2+20x=90

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


Simplifying
x2 + 20x = 90

Reorder the terms:
20x + x2 = 90

Solving
20x + x2 = 90

Solving for variable 'x'.

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

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

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 = 190
100 + 20x + x2 = 190

Factor a perfect square on the left side:
(x + 10)(x + 10) = 190

Calculate the square root of the right side: 13.784048752

Break this problem into two subproblems by setting 
(x + 10) equal to 13.784048752 and -13.784048752.

Subproblem 1

x + 10 = 13.784048752 Simplifying x + 10 = 13.784048752 Reorder the terms: 10 + x = 13.784048752 Solving 10 + x = 13.784048752 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 = 13.784048752 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.784048752 + -10 x = 13.784048752 + -10 Combine like terms: 13.784048752 + -10 = 3.784048752 x = 3.784048752 Simplifying x = 3.784048752

Subproblem 2

x + 10 = -13.784048752 Simplifying x + 10 = -13.784048752 Reorder the terms: 10 + x = -13.784048752 Solving 10 + x = -13.784048752 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 = -13.784048752 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.784048752 + -10 x = -13.784048752 + -10 Combine like terms: -13.784048752 + -10 = -23.784048752 x = -23.784048752 Simplifying x = -23.784048752

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.784048752, -23.784048752}

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