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Simplifying 6x2 + 16x + -12 = 0 Reorder the terms: -12 + 16x + 6x2 = 0 Solving -12 + 16x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 8x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + 8x + 3x2 = 0 Solving -6 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.666666667x + x2 = 0 + 2 2.666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.666666667x + x2 = 2 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 2 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 2 + 1.777777780 Combine like terms: 2 + 1.777777780 = 3.77777778 1.777777780 + 2.666666667x + x2 = 3.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 3.77777778 Calculate the square root of the right side: 1.943650632 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.943650632 and -1.943650632.Subproblem 1
x + 1.333333334 = 1.943650632 Simplifying x + 1.333333334 = 1.943650632 Reorder the terms: 1.333333334 + x = 1.943650632 Solving 1.333333334 + x = 1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.943650632 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.943650632 + -1.333333334 x = 1.943650632 + -1.333333334 Combine like terms: 1.943650632 + -1.333333334 = 0.610317298 x = 0.610317298 Simplifying x = 0.610317298Subproblem 2
x + 1.333333334 = -1.943650632 Simplifying x + 1.333333334 = -1.943650632 Reorder the terms: 1.333333334 + x = -1.943650632 Solving 1.333333334 + x = -1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.943650632 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.943650632 + -1.333333334 x = -1.943650632 + -1.333333334 Combine like terms: -1.943650632 + -1.333333334 = -3.276983966 x = -3.276983966 Simplifying x = -3.276983966Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.610317298, -3.276983966}Solution
x = {0.610317298, -3.276983966}
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