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Simplifying 12x2 + -68x + 42 = 0 Reorder the terms: 42 + -68x + 12x2 = 0 Solving 42 + -68x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -34x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + -34x + 6x2)' equal to zero and attempt to solve: Simplifying 21 + -34x + 6x2 = 0 Solving 21 + -34x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.5 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -5.666666667x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -5.666666667x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -5.666666667x + x2 = 0 + -3.5 -5.666666667x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -5.666666667x + x2 = -3.5 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = -3.5 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = -3.5 + 8.027777782 Combine like terms: -3.5 + 8.027777782 = 4.527777782 8.027777782 + -5.666666667x + x2 = 4.527777782 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 4.527777782 Calculate the square root of the right side: 2.127857557 Break this problem into two subproblems by setting (x + -2.833333334) equal to 2.127857557 and -2.127857557.Subproblem 1
x + -2.833333334 = 2.127857557 Simplifying x + -2.833333334 = 2.127857557 Reorder the terms: -2.833333334 + x = 2.127857557 Solving -2.833333334 + x = 2.127857557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 2.127857557 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 2.127857557 + 2.833333334 x = 2.127857557 + 2.833333334 Combine like terms: 2.127857557 + 2.833333334 = 4.961190891 x = 4.961190891 Simplifying x = 4.961190891Subproblem 2
x + -2.833333334 = -2.127857557 Simplifying x + -2.833333334 = -2.127857557 Reorder the terms: -2.833333334 + x = -2.127857557 Solving -2.833333334 + x = -2.127857557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -2.127857557 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -2.127857557 + 2.833333334 x = -2.127857557 + 2.833333334 Combine like terms: -2.127857557 + 2.833333334 = 0.705475777 x = 0.705475777 Simplifying x = 0.705475777Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.961190891, 0.705475777}Solution
x = {4.961190891, 0.705475777}
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