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Simplifying 10x2 + -500x = -4320 Reorder the terms: -500x + 10x2 = -4320 Solving -500x + 10x2 = -4320 Solving for variable 'x'. Reorder the terms: 4320 + -500x + 10x2 = -4320 + 4320 Combine like terms: -4320 + 4320 = 0 4320 + -500x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(432 + -50x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(432 + -50x + x2)' equal to zero and attempt to solve: Simplifying 432 + -50x + x2 = 0 Solving 432 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-432' to each side of the equation. 432 + -50x + -432 + x2 = 0 + -432 Reorder the terms: 432 + -432 + -50x + x2 = 0 + -432 Combine like terms: 432 + -432 = 0 0 + -50x + x2 = 0 + -432 -50x + x2 = 0 + -432 Combine like terms: 0 + -432 = -432 -50x + x2 = -432 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -432 + 625 Reorder the terms: 625 + -50x + x2 = -432 + 625 Combine like terms: -432 + 625 = 193 625 + -50x + x2 = 193 Factor a perfect square on the left side: (x + -25)(x + -25) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + -25) equal to 13.892443989 and -13.892443989.Subproblem 1
x + -25 = 13.892443989 Simplifying x + -25 = 13.892443989 Reorder the terms: -25 + x = 13.892443989 Solving -25 + x = 13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 13.892443989 + 25 Combine like terms: -25 + 25 = 0 0 + x = 13.892443989 + 25 x = 13.892443989 + 25 Combine like terms: 13.892443989 + 25 = 38.892443989 x = 38.892443989 Simplifying x = 38.892443989Subproblem 2
x + -25 = -13.892443989 Simplifying x + -25 = -13.892443989 Reorder the terms: -25 + x = -13.892443989 Solving -25 + x = -13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -13.892443989 + 25 Combine like terms: -25 + 25 = 0 0 + x = -13.892443989 + 25 x = -13.892443989 + 25 Combine like terms: -13.892443989 + 25 = 11.107556011 x = 11.107556011 Simplifying x = 11.107556011Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.892443989, 11.107556011}Solution
x = {38.892443989, 11.107556011}
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