x(x)+2x-3=129

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Solution for x(x)+2x-3=129 equation:


Simplifying
x(x) + 2x + -3 = 129

Multiply x * x
x2 + 2x + -3 = 129

Reorder the terms:
-3 + 2x + x2 = 129

Solving
-3 + 2x + x2 = 129

Solving for variable 'x'.

Reorder the terms:
-3 + -129 + 2x + x2 = 129 + -129

Combine like terms: -3 + -129 = -132
-132 + 2x + x2 = 129 + -129

Combine like terms: 129 + -129 = 0
-132 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '132' to each side of the equation.
-132 + 2x + 132 + x2 = 0 + 132

Reorder the terms:
-132 + 132 + 2x + x2 = 0 + 132

Combine like terms: -132 + 132 = 0
0 + 2x + x2 = 0 + 132
2x + x2 = 0 + 132

Combine like terms: 0 + 132 = 132
2x + x2 = 132

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 132 + 1

Reorder the terms:
1 + 2x + x2 = 132 + 1

Combine like terms: 132 + 1 = 133
1 + 2x + x2 = 133

Factor a perfect square on the left side:
(x + 1)(x + 1) = 133

Calculate the square root of the right side: 11.532562595

Break this problem into two subproblems by setting 
(x + 1) equal to 11.532562595 and -11.532562595.

Subproblem 1

x + 1 = 11.532562595 Simplifying x + 1 = 11.532562595 Reorder the terms: 1 + x = 11.532562595 Solving 1 + x = 11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 11.532562595 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.532562595 + -1 x = 11.532562595 + -1 Combine like terms: 11.532562595 + -1 = 10.532562595 x = 10.532562595 Simplifying x = 10.532562595

Subproblem 2

x + 1 = -11.532562595 Simplifying x + 1 = -11.532562595 Reorder the terms: 1 + x = -11.532562595 Solving 1 + x = -11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -11.532562595 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.532562595 + -1 x = -11.532562595 + -1 Combine like terms: -11.532562595 + -1 = -12.532562595 x = -12.532562595 Simplifying x = -12.532562595

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.532562595, -12.532562595}

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