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Simplifying -2x2 + 200x = 1500 Reorder the terms: 200x + -2x2 = 1500 Solving 200x + -2x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 200x + -2x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 200x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-750 + 100x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-750 + 100x + -1x2)' equal to zero and attempt to solve: Simplifying -750 + 100x + -1x2 = 0 Solving -750 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 750 + -100x + x2 = 0 Move the constant term to the right: Add '-750' to each side of the equation. 750 + -100x + -750 + x2 = 0 + -750 Reorder the terms: 750 + -750 + -100x + x2 = 0 + -750 Combine like terms: 750 + -750 = 0 0 + -100x + x2 = 0 + -750 -100x + x2 = 0 + -750 Combine like terms: 0 + -750 = -750 -100x + x2 = -750 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -750 + 2500 Reorder the terms: 2500 + -100x + x2 = -750 + 2500 Combine like terms: -750 + 2500 = 1750 2500 + -100x + x2 = 1750 Factor a perfect square on the left side: (x + -50)(x + -50) = 1750 Calculate the square root of the right side: 41.833001327 Break this problem into two subproblems by setting (x + -50) equal to 41.833001327 and -41.833001327.Subproblem 1
x + -50 = 41.833001327 Simplifying x + -50 = 41.833001327 Reorder the terms: -50 + x = 41.833001327 Solving -50 + x = 41.833001327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 41.833001327 + 50 Combine like terms: -50 + 50 = 0 0 + x = 41.833001327 + 50 x = 41.833001327 + 50 Combine like terms: 41.833001327 + 50 = 91.833001327 x = 91.833001327 Simplifying x = 91.833001327Subproblem 2
x + -50 = -41.833001327 Simplifying x + -50 = -41.833001327 Reorder the terms: -50 + x = -41.833001327 Solving -50 + x = -41.833001327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -41.833001327 + 50 Combine like terms: -50 + 50 = 0 0 + x = -41.833001327 + 50 x = -41.833001327 + 50 Combine like terms: -41.833001327 + 50 = 8.166998673 x = 8.166998673 Simplifying x = 8.166998673Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.833001327, 8.166998673}Solution
x = {91.833001327, 8.166998673}
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