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Simplifying 12x2 + 74x + -910 = 0 Reorder the terms: -910 + 74x + 12x2 = 0 Solving -910 + 74x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-455 + 37x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-455 + 37x + 6x2)' equal to zero and attempt to solve: Simplifying -455 + 37x + 6x2 = 0 Solving -455 + 37x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -75.83333333 + 6.166666667x + x2 = 0 Move the constant term to the right: Add '75.83333333' to each side of the equation. -75.83333333 + 6.166666667x + 75.83333333 + x2 = 0 + 75.83333333 Reorder the terms: -75.83333333 + 75.83333333 + 6.166666667x + x2 = 0 + 75.83333333 Combine like terms: -75.83333333 + 75.83333333 = 0.00000000 0.00000000 + 6.166666667x + x2 = 0 + 75.83333333 6.166666667x + x2 = 0 + 75.83333333 Combine like terms: 0 + 75.83333333 = 75.83333333 6.166666667x + x2 = 75.83333333 The x term is 6.166666667x. Take half its coefficient (3.083333334). Square it (9.506944449) and add it to both sides. Add '9.506944449' to each side of the equation. 6.166666667x + 9.506944449 + x2 = 75.83333333 + 9.506944449 Reorder the terms: 9.506944449 + 6.166666667x + x2 = 75.83333333 + 9.506944449 Combine like terms: 75.83333333 + 9.506944449 = 85.340277779 9.506944449 + 6.166666667x + x2 = 85.340277779 Factor a perfect square on the left side: (x + 3.083333334)(x + 3.083333334) = 85.340277779 Calculate the square root of the right side: 9.237980179 Break this problem into two subproblems by setting (x + 3.083333334) equal to 9.237980179 and -9.237980179.Subproblem 1
x + 3.083333334 = 9.237980179 Simplifying x + 3.083333334 = 9.237980179 Reorder the terms: 3.083333334 + x = 9.237980179 Solving 3.083333334 + x = 9.237980179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.083333334' to each side of the equation. 3.083333334 + -3.083333334 + x = 9.237980179 + -3.083333334 Combine like terms: 3.083333334 + -3.083333334 = 0.000000000 0.000000000 + x = 9.237980179 + -3.083333334 x = 9.237980179 + -3.083333334 Combine like terms: 9.237980179 + -3.083333334 = 6.154646845 x = 6.154646845 Simplifying x = 6.154646845Subproblem 2
x + 3.083333334 = -9.237980179 Simplifying x + 3.083333334 = -9.237980179 Reorder the terms: 3.083333334 + x = -9.237980179 Solving 3.083333334 + x = -9.237980179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.083333334' to each side of the equation. 3.083333334 + -3.083333334 + x = -9.237980179 + -3.083333334 Combine like terms: 3.083333334 + -3.083333334 = 0.000000000 0.000000000 + x = -9.237980179 + -3.083333334 x = -9.237980179 + -3.083333334 Combine like terms: -9.237980179 + -3.083333334 = -12.321313513 x = -12.321313513 Simplifying x = -12.321313513Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.154646845, -12.321313513}Solution
x = {6.154646845, -12.321313513}
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