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Simplifying 12x2 + 38x + -16 = 0 Reorder the terms: -16 + 38x + 12x2 = 0 Solving -16 + 38x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 19x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 19x + 6x2)' equal to zero and attempt to solve: Simplifying -8 + 19x + 6x2 = 0 Solving -8 + 19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 3.166666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 3.166666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 3.166666667x + x2 = 0 + 1.333333333 3.166666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 3.166666667x + x2 = 1.333333333 The x term is 3.166666667x. Take half its coefficient (1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. 3.166666667x + 2.506944447 + x2 = 1.333333333 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = 1.333333333 + 2.506944447 Combine like terms: 1.333333333 + 2.506944447 = 3.84027778 2.506944447 + 3.166666667x + x2 = 3.84027778 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 3.84027778 Calculate the square root of the right side: 1.95966267 Break this problem into two subproblems by setting (x + 1.583333334) equal to 1.95966267 and -1.95966267.Subproblem 1
x + 1.583333334 = 1.95966267 Simplifying x + 1.583333334 = 1.95966267 Reorder the terms: 1.583333334 + x = 1.95966267 Solving 1.583333334 + x = 1.95966267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + x = 1.95966267 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 1.95966267 + -1.583333334 x = 1.95966267 + -1.583333334 Combine like terms: 1.95966267 + -1.583333334 = 0.376329336 x = 0.376329336 Simplifying x = 0.376329336Subproblem 2
x + 1.583333334 = -1.95966267 Simplifying x + 1.583333334 = -1.95966267 Reorder the terms: 1.583333334 + x = -1.95966267 Solving 1.583333334 + x = -1.95966267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + x = -1.95966267 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -1.95966267 + -1.583333334 x = -1.95966267 + -1.583333334 Combine like terms: -1.95966267 + -1.583333334 = -3.542996004 x = -3.542996004 Simplifying x = -3.542996004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.376329336, -3.542996004}Solution
x = {0.376329336, -3.542996004}
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