x(x-1)=153

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Solution for x(x-1)=153 equation:


Simplifying
x(x + -1) = 153

Reorder the terms:
x(-1 + x) = 153
(-1 * x + x * x) = 153
(-1x + x2) = 153

Solving
-1x + x2 = 153

Solving for variable 'x'.

Reorder the terms:
-153 + -1x + x2 = 153 + -153

Combine like terms: 153 + -153 = 0
-153 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '153' to each side of the equation.
-153 + -1x + 153 + x2 = 0 + 153

Reorder the terms:
-153 + 153 + -1x + x2 = 0 + 153

Combine like terms: -153 + 153 = 0
0 + -1x + x2 = 0 + 153
-1x + x2 = 0 + 153

Combine like terms: 0 + 153 = 153
-1x + x2 = 153

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 = 153 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 153 + 0.25

Combine like terms: 153 + 0.25 = 153.25
0.25 + -1x + x2 = 153.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 153.25

Calculate the square root of the right side: 12.379418403

Break this problem into two subproblems by setting 
(x + -0.5) equal to 12.379418403 and -12.379418403.

Subproblem 1

x + -0.5 = 12.379418403 Simplifying x + -0.5 = 12.379418403 Reorder the terms: -0.5 + x = 12.379418403 Solving -0.5 + x = 12.379418403 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 = 12.379418403 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 12.379418403 + 0.5 x = 12.379418403 + 0.5 Combine like terms: 12.379418403 + 0.5 = 12.879418403 x = 12.879418403 Simplifying x = 12.879418403

Subproblem 2

x + -0.5 = -12.379418403 Simplifying x + -0.5 = -12.379418403 Reorder the terms: -0.5 + x = -12.379418403 Solving -0.5 + x = -12.379418403 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 = -12.379418403 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -12.379418403 + 0.5 x = -12.379418403 + 0.5 Combine like terms: -12.379418403 + 0.5 = -11.879418403 x = -11.879418403 Simplifying x = -11.879418403

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.879418403, -11.879418403}

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