x(x-1)=142

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Solution for x(x-1)=142 equation:


Simplifying
x(x + -1) = 142

Reorder the terms:
x(-1 + x) = 142
(-1 * x + x * x) = 142
(-1x + x2) = 142

Solving
-1x + x2 = 142

Solving for variable 'x'.

Reorder the terms:
-142 + -1x + x2 = 142 + -142

Combine like terms: 142 + -142 = 0
-142 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '142' to each side of the equation.
-142 + -1x + 142 + x2 = 0 + 142

Reorder the terms:
-142 + 142 + -1x + x2 = 0 + 142

Combine like terms: -142 + 142 = 0
0 + -1x + x2 = 0 + 142
-1x + x2 = 0 + 142

Combine like terms: 0 + 142 = 142
-1x + x2 = 142

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 = 142 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 142 + 0.25

Combine like terms: 142 + 0.25 = 142.25
0.25 + -1x + x2 = 142.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(x + -0.5) equal to 11.926860442 and -11.926860442.

Subproblem 1

x + -0.5 = 11.926860442 Simplifying x + -0.5 = 11.926860442 Reorder the terms: -0.5 + x = 11.926860442 Solving -0.5 + x = 11.926860442 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 = 11.926860442 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 11.926860442 + 0.5 x = 11.926860442 + 0.5 Combine like terms: 11.926860442 + 0.5 = 12.426860442 x = 12.426860442 Simplifying x = 12.426860442

Subproblem 2

x + -0.5 = -11.926860442 Simplifying x + -0.5 = -11.926860442 Reorder the terms: -0.5 + x = -11.926860442 Solving -0.5 + x = -11.926860442 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 = -11.926860442 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -11.926860442 + 0.5 x = -11.926860442 + 0.5 Combine like terms: -11.926860442 + 0.5 = -11.426860442 x = -11.426860442 Simplifying x = -11.426860442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.426860442, -11.426860442}

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