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Simplifying 12x2 + -28 = 38x Reorder the terms: -28 + 12x2 = 38x Solving -28 + 12x2 = 38x Solving for variable 'x'. Reorder the terms: -28 + -38x + 12x2 = 38x + -38x Combine like terms: 38x + -38x = 0 -28 + -38x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -19x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -19x + 6x2)' equal to zero and attempt to solve: Simplifying -14 + -19x + 6x2 = 0 Solving -14 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.333333333 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -3.166666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -3.166666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + 2.333333333 -3.166666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -3.166666667x + x2 = 2.333333333 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 = 2.333333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 2.333333333 + 2.506944447 Combine like terms: 2.333333333 + 2.506944447 = 4.84027778 2.506944447 + -3.166666667x + x2 = 4.84027778 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 4.84027778 Calculate the square root of the right side: 2.200063131 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.200063131 and -2.200063131.Subproblem 1
x + -1.583333334 = 2.200063131 Simplifying x + -1.583333334 = 2.200063131 Reorder the terms: -1.583333334 + x = 2.200063131 Solving -1.583333334 + x = 2.200063131 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 = 2.200063131 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.200063131 + 1.583333334 x = 2.200063131 + 1.583333334 Combine like terms: 2.200063131 + 1.583333334 = 3.783396465 x = 3.783396465 Simplifying x = 3.783396465Subproblem 2
x + -1.583333334 = -2.200063131 Simplifying x + -1.583333334 = -2.200063131 Reorder the terms: -1.583333334 + x = -2.200063131 Solving -1.583333334 + x = -2.200063131 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 = -2.200063131 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.200063131 + 1.583333334 x = -2.200063131 + 1.583333334 Combine like terms: -2.200063131 + 1.583333334 = -0.616729797 x = -0.616729797 Simplifying x = -0.616729797Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.783396465, -0.616729797}Solution
x = {3.783396465, -0.616729797}
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