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Simplifying 36x2 + -480x + -2462 = 0 Reorder the terms: -2462 + -480x + 36x2 = 0 Solving -2462 + -480x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1231 + -240x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1231 + -240x + 18x2)' equal to zero and attempt to solve: Simplifying -1231 + -240x + 18x2 = 0 Solving -1231 + -240x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -68.38888889 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '68.38888889' to each side of the equation. -68.38888889 + -13.33333333x + 68.38888889 + x2 = 0 + 68.38888889 Reorder the terms: -68.38888889 + 68.38888889 + -13.33333333x + x2 = 0 + 68.38888889 Combine like terms: -68.38888889 + 68.38888889 = 0.00000000 0.00000000 + -13.33333333x + x2 = 0 + 68.38888889 -13.33333333x + x2 = 0 + 68.38888889 Combine like terms: 0 + 68.38888889 = 68.38888889 -13.33333333x + x2 = 68.38888889 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = 68.38888889 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 68.38888889 + 44.44444442 Combine like terms: 68.38888889 + 44.44444442 = 112.83333331 44.44444442 + -13.33333333x + x2 = 112.83333331 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 112.83333331 Calculate the square root of the right side: 10.622303578 Break this problem into two subproblems by setting (x + -6.666666665) equal to 10.622303578 and -10.622303578.Subproblem 1
x + -6.666666665 = 10.622303578 Simplifying x + -6.666666665 = 10.622303578 Reorder the terms: -6.666666665 + x = 10.622303578 Solving -6.666666665 + x = 10.622303578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 10.622303578 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 10.622303578 + 6.666666665 x = 10.622303578 + 6.666666665 Combine like terms: 10.622303578 + 6.666666665 = 17.288970243 x = 17.288970243 Simplifying x = 17.288970243Subproblem 2
x + -6.666666665 = -10.622303578 Simplifying x + -6.666666665 = -10.622303578 Reorder the terms: -6.666666665 + x = -10.622303578 Solving -6.666666665 + x = -10.622303578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -10.622303578 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -10.622303578 + 6.666666665 x = -10.622303578 + 6.666666665 Combine like terms: -10.622303578 + 6.666666665 = -3.955636913 x = -3.955636913 Simplifying x = -3.955636913Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.288970243, -3.955636913}Solution
x = {17.288970243, -3.955636913}
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