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Simplifying 12x2 + -92x + 126 = 0 Reorder the terms: 126 + -92x + 12x2 = 0 Solving 126 + -92x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(63 + -46x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(63 + -46x + 6x2)' equal to zero and attempt to solve: Simplifying 63 + -46x + 6x2 = 0 Solving 63 + -46x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 10.5 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -7.666666667x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -7.666666667x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -7.666666667x + x2 = 0 + -10.5 -7.666666667x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -7.666666667x + x2 = -10.5 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = -10.5 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -10.5 + 14.69444445 Combine like terms: -10.5 + 14.69444445 = 4.19444445 14.69444445 + -7.666666667x + x2 = 4.19444445 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 4.19444445 Calculate the square root of the right side: 2.048034289 Break this problem into two subproblems by setting (x + -3.833333334) equal to 2.048034289 and -2.048034289.Subproblem 1
x + -3.833333334 = 2.048034289 Simplifying x + -3.833333334 = 2.048034289 Reorder the terms: -3.833333334 + x = 2.048034289 Solving -3.833333334 + x = 2.048034289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 2.048034289 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 2.048034289 + 3.833333334 x = 2.048034289 + 3.833333334 Combine like terms: 2.048034289 + 3.833333334 = 5.881367623 x = 5.881367623 Simplifying x = 5.881367623Subproblem 2
x + -3.833333334 = -2.048034289 Simplifying x + -3.833333334 = -2.048034289 Reorder the terms: -3.833333334 + x = -2.048034289 Solving -3.833333334 + x = -2.048034289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -2.048034289 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -2.048034289 + 3.833333334 x = -2.048034289 + 3.833333334 Combine like terms: -2.048034289 + 3.833333334 = 1.785299045 x = 1.785299045 Simplifying x = 1.785299045Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.881367623, 1.785299045}Solution
x = {5.881367623, 1.785299045}
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