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Simplifying 6x * x + -4x + -12 = -2x Multiply x * x 6x2 + -4x + -12 = -2x Reorder the terms: -12 + -4x + 6x2 = -2x Solving -12 + -4x + 6x2 = -2x Solving for variable 'x'. Reorder the terms: -12 + -4x + 2x + 6x2 = -2x + 2x Combine like terms: -4x + 2x = -2x -12 + -2x + 6x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -12 + -2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -1x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + -1x + 3x2 = 0 Solving -6 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.3333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.3333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.3333333333x + x2 = 0 + 2 -0.3333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.3333333333x + x2 = 2 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 2 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 2 + 0.02777777779 Combine like terms: 2 + 0.02777777779 = 2.02777777779 0.02777777779 + -0.3333333333x + x2 = 2.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 2.02777777779 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.424000624 and -1.424000624.Subproblem 1
x + -0.1666666667 = 1.424000624 Simplifying x + -0.1666666667 = 1.424000624 Reorder the terms: -0.1666666667 + x = 1.424000624 Solving -0.1666666667 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.424000624 + 0.1666666667 x = 1.424000624 + 0.1666666667 Combine like terms: 1.424000624 + 0.1666666667 = 1.5906672907 x = 1.5906672907 Simplifying x = 1.5906672907Subproblem 2
x + -0.1666666667 = -1.424000624 Simplifying x + -0.1666666667 = -1.424000624 Reorder the terms: -0.1666666667 + x = -1.424000624 Solving -0.1666666667 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.424000624 + 0.1666666667 x = -1.424000624 + 0.1666666667 Combine like terms: -1.424000624 + 0.1666666667 = -1.2573339573 x = -1.2573339573 Simplifying x = -1.2573339573Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5906672907, -1.2573339573}Solution
x = {1.5906672907, -1.2573339573}
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