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Simplifying 5x(12x + -41) = 180 Reorder the terms: 5x(-41 + 12x) = 180 (-41 * 5x + 12x * 5x) = 180 (-205x + 60x2) = 180 Solving -205x + 60x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -205x + 60x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -205x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + -41x + 12x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + -41x + 12x2)' equal to zero and attempt to solve: Simplifying -36 + -41x + 12x2 = 0 Solving -36 + -41x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3 + -3.416666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.416666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -3.416666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.416666667x + x2 = 0 + 3 -3.416666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.416666667x + x2 = 3 The x term is -3.416666667x. Take half its coefficient (-1.708333334). Square it (2.918402780) and add it to both sides. Add '2.918402780' to each side of the equation. -3.416666667x + 2.918402780 + x2 = 3 + 2.918402780 Reorder the terms: 2.918402780 + -3.416666667x + x2 = 3 + 2.918402780 Combine like terms: 3 + 2.918402780 = 5.91840278 2.918402780 + -3.416666667x + x2 = 5.91840278 Factor a perfect square on the left side: (x + -1.708333334)(x + -1.708333334) = 5.91840278 Calculate the square root of the right side: 2.432776763 Break this problem into two subproblems by setting (x + -1.708333334) equal to 2.432776763 and -2.432776763.Subproblem 1
x + -1.708333334 = 2.432776763 Simplifying x + -1.708333334 = 2.432776763 Reorder the terms: -1.708333334 + x = 2.432776763 Solving -1.708333334 + x = 2.432776763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.708333334' to each side of the equation. -1.708333334 + 1.708333334 + x = 2.432776763 + 1.708333334 Combine like terms: -1.708333334 + 1.708333334 = 0.000000000 0.000000000 + x = 2.432776763 + 1.708333334 x = 2.432776763 + 1.708333334 Combine like terms: 2.432776763 + 1.708333334 = 4.141110097 x = 4.141110097 Simplifying x = 4.141110097Subproblem 2
x + -1.708333334 = -2.432776763 Simplifying x + -1.708333334 = -2.432776763 Reorder the terms: -1.708333334 + x = -2.432776763 Solving -1.708333334 + x = -2.432776763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.708333334' to each side of the equation. -1.708333334 + 1.708333334 + x = -2.432776763 + 1.708333334 Combine like terms: -1.708333334 + 1.708333334 = 0.000000000 0.000000000 + x = -2.432776763 + 1.708333334 x = -2.432776763 + 1.708333334 Combine like terms: -2.432776763 + 1.708333334 = -0.724443429 x = -0.724443429 Simplifying x = -0.724443429Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.141110097, -0.724443429}Solution
x = {4.141110097, -0.724443429}
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