126=6x(x-2)

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Solution for 126=6x(x-2) equation:


Simplifying
126 = 6x(x + -2)

Reorder the terms:
126 = 6x(-2 + x)
126 = (-2 * 6x + x * 6x)
126 = (-12x + 6x2)

Solving
126 = -12x + 6x2

Solving for variable 'x'.

Reorder the terms:
126 + 12x + -6x2 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
126 + 12x + -6x2 = 0 + 6x2 + -6x2
126 + 12x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
126 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(21 + 2x + -1x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(21 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 21 + 2x + -1x2 = 0 Solving 21 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -2x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -2x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -2x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2x + x2 = 0 + 21 -2x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2x + x2 = 21 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 = 21 + 1 Reorder the terms: 1 + -2x + x2 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + -2x + x2 = 22 Factor a perfect square on the left side: (x + -1)(x + -1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -1) equal to 4.69041576 and -4.69041576.

Subproblem 1

x + -1 = 4.69041576 Simplifying x + -1 = 4.69041576 Reorder the terms: -1 + x = 4.69041576 Solving -1 + x = 4.69041576 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 = 4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.69041576 + 1 x = 4.69041576 + 1 Combine like terms: 4.69041576 + 1 = 5.69041576 x = 5.69041576 Simplifying x = 5.69041576

Subproblem 2

x + -1 = -4.69041576 Simplifying x + -1 = -4.69041576 Reorder the terms: -1 + x = -4.69041576 Solving -1 + x = -4.69041576 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 = -4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.69041576 + 1 x = -4.69041576 + 1 Combine like terms: -4.69041576 + 1 = -3.69041576 x = -3.69041576 Simplifying x = -3.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.69041576, -3.69041576}

Solution

x = {5.69041576, -3.69041576}

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