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Simplifying 12x2 + -92x + 112 = 0 Reorder the terms: 112 + -92x + 12x2 = 0 Solving 112 + -92x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(28 + -23x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(28 + -23x + 3x2)' equal to zero and attempt to solve: Simplifying 28 + -23x + 3x2 = 0 Solving 28 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9.333333333 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + -7.666666667x + -9.333333333 + x2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + -7.666666667x + x2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + -9.333333333 -7.666666667x + x2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 -7.666666667x + x2 = -9.333333333 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 = -9.333333333 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -9.333333333 + 14.69444445 Combine like terms: -9.333333333 + 14.69444445 = 5.361111117 14.69444445 + -7.666666667x + x2 = 5.361111117 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 5.361111117 Calculate the square root of the right side: 2.315407333 Break this problem into two subproblems by setting (x + -3.833333334) equal to 2.315407333 and -2.315407333.Subproblem 1
x + -3.833333334 = 2.315407333 Simplifying x + -3.833333334 = 2.315407333 Reorder the terms: -3.833333334 + x = 2.315407333 Solving -3.833333334 + x = 2.315407333 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 = 2.315407333 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 2.315407333 + 3.833333334 x = 2.315407333 + 3.833333334 Combine like terms: 2.315407333 + 3.833333334 = 6.148740667 x = 6.148740667 Simplifying x = 6.148740667Subproblem 2
x + -3.833333334 = -2.315407333 Simplifying x + -3.833333334 = -2.315407333 Reorder the terms: -3.833333334 + x = -2.315407333 Solving -3.833333334 + x = -2.315407333 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 = -2.315407333 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -2.315407333 + 3.833333334 x = -2.315407333 + 3.833333334 Combine like terms: -2.315407333 + 3.833333334 = 1.517926001 x = 1.517926001 Simplifying x = 1.517926001Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.148740667, 1.517926001}Solution
x = {6.148740667, 1.517926001}
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