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Simplifying 12x2 + -38x + 14 = 0 Reorder the terms: 14 + -38x + 12x2 = 0 Solving 14 + -38x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -19x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -19x + 6x2)' equal to zero and attempt to solve: Simplifying 7 + -19x + 6x2 = 0 Solving 7 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -3.166666667x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -3.166666667x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + -1.166666667 -3.166666667x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -3.166666667x + x2 = -1.166666667 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 = -1.166666667 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = -1.166666667 + 2.506944447 Combine like terms: -1.166666667 + 2.506944447 = 1.34027778 2.506944447 + -3.166666667x + x2 = 1.34027778 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 1.34027778 Calculate the square root of the right side: 1.157703667 Break this problem into two subproblems by setting (x + -1.583333334) equal to 1.157703667 and -1.157703667.Subproblem 1
x + -1.583333334 = 1.157703667 Simplifying x + -1.583333334 = 1.157703667 Reorder the terms: -1.583333334 + x = 1.157703667 Solving -1.583333334 + x = 1.157703667 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 = 1.157703667 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 1.157703667 + 1.583333334 x = 1.157703667 + 1.583333334 Combine like terms: 1.157703667 + 1.583333334 = 2.741037001 x = 2.741037001 Simplifying x = 2.741037001Subproblem 2
x + -1.583333334 = -1.157703667 Simplifying x + -1.583333334 = -1.157703667 Reorder the terms: -1.583333334 + x = -1.157703667 Solving -1.583333334 + x = -1.157703667 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 = -1.157703667 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -1.157703667 + 1.583333334 x = -1.157703667 + 1.583333334 Combine like terms: -1.157703667 + 1.583333334 = 0.425629667 x = 0.425629667 Simplifying x = 0.425629667Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.741037001, 0.425629667}Solution
x = {2.741037001, 0.425629667}
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