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Simplifying -200x2 + 3600x + -6400 + -8500 = 0 Reorder the terms: -6400 + -8500 + 3600x + -200x2 = 0 Combine like terms: -6400 + -8500 = -14900 -14900 + 3600x + -200x2 = 0 Solving -14900 + 3600x + -200x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '100'. 100(-149 + 36x + -2x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-149 + 36x + -2x2)' equal to zero and attempt to solve: Simplifying -149 + 36x + -2x2 = 0 Solving -149 + 36x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 74.5 + -18x + x2 = 0 Move the constant term to the right: Add '-74.5' to each side of the equation. 74.5 + -18x + -74.5 + x2 = 0 + -74.5 Reorder the terms: 74.5 + -74.5 + -18x + x2 = 0 + -74.5 Combine like terms: 74.5 + -74.5 = 0.0 0.0 + -18x + x2 = 0 + -74.5 -18x + x2 = 0 + -74.5 Combine like terms: 0 + -74.5 = -74.5 -18x + x2 = -74.5 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -74.5 + 81 Reorder the terms: 81 + -18x + x2 = -74.5 + 81 Combine like terms: -74.5 + 81 = 6.5 81 + -18x + x2 = 6.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -9) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -9 = 2.549509757 Simplifying x + -9 = 2.549509757 Reorder the terms: -9 + x = 2.549509757 Solving -9 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 2.549509757 + 9 Combine like terms: -9 + 9 = 0 0 + x = 2.549509757 + 9 x = 2.549509757 + 9 Combine like terms: 2.549509757 + 9 = 11.549509757 x = 11.549509757 Simplifying x = 11.549509757Subproblem 2
x + -9 = -2.549509757 Simplifying x + -9 = -2.549509757 Reorder the terms: -9 + x = -2.549509757 Solving -9 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -2.549509757 + 9 Combine like terms: -9 + 9 = 0 0 + x = -2.549509757 + 9 x = -2.549509757 + 9 Combine like terms: -2.549509757 + 9 = 6.450490243 x = 6.450490243 Simplifying x = 6.450490243Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.549509757, 6.450490243}Solution
x = {11.549509757, 6.450490243}
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