x(x-1)-20=20

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Solution for x(x-1)-20=20 equation:


Simplifying
x(x + -1) + -20 = 20

Reorder the terms:
x(-1 + x) + -20 = 20
(-1 * x + x * x) + -20 = 20
(-1x + x2) + -20 = 20

Reorder the terms:
-20 + -1x + x2 = 20

Solving
-20 + -1x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -20 + -1x + x2 = 20 + -20

Combine like terms: -20 + -20 = -40
-40 + -1x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-40 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -1x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -1x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1x + x2 = 0 + 40
-1x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-1x + x2 = 40

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 40 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 40 + 0.25

Combine like terms: 40 + 0.25 = 40.25
0.25 + -1x + x2 = 40.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -0.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

x + -0.5 = 6.34428877 Simplifying x + -0.5 = 6.34428877 Reorder the terms: -0.5 + x = 6.34428877 Solving -0.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.34428877 + 0.5 x = 6.34428877 + 0.5 Combine like terms: 6.34428877 + 0.5 = 6.84428877 x = 6.84428877 Simplifying x = 6.84428877

Subproblem 2

x + -0.5 = -6.34428877 Simplifying x + -0.5 = -6.34428877 Reorder the terms: -0.5 + x = -6.34428877 Solving -0.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.34428877 + 0.5 x = -6.34428877 + 0.5 Combine like terms: -6.34428877 + 0.5 = -5.84428877 x = -5.84428877 Simplifying x = -5.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.84428877, -5.84428877}

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