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Simplifying -4x2 + 200x + 150 = 0 Reorder the terms: 150 + 200x + -4x2 = 0 Solving 150 + 200x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + 100x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + 100x + -2x2)' equal to zero and attempt to solve: Simplifying 75 + 100x + -2x2 = 0 Solving 75 + 100x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -37.5 + -50x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + -50x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + -50x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + -50x + x2 = 0 + 37.5 -50x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 -50x + x2 = 37.5 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 = 37.5 + 625 Reorder the terms: 625 + -50x + x2 = 37.5 + 625 Combine like terms: 37.5 + 625 = 662.5 625 + -50x + x2 = 662.5 Factor a perfect square on the left side: (x + -25)(x + -25) = 662.5 Calculate the square root of the right side: 25.739075352 Break this problem into two subproblems by setting (x + -25) equal to 25.739075352 and -25.739075352.Subproblem 1
x + -25 = 25.739075352 Simplifying x + -25 = 25.739075352 Reorder the terms: -25 + x = 25.739075352 Solving -25 + x = 25.739075352 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 = 25.739075352 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.739075352 + 25 x = 25.739075352 + 25 Combine like terms: 25.739075352 + 25 = 50.739075352 x = 50.739075352 Simplifying x = 50.739075352Subproblem 2
x + -25 = -25.739075352 Simplifying x + -25 = -25.739075352 Reorder the terms: -25 + x = -25.739075352 Solving -25 + x = -25.739075352 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 = -25.739075352 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.739075352 + 25 x = -25.739075352 + 25 Combine like terms: -25.739075352 + 25 = -0.739075352 x = -0.739075352 Simplifying x = -0.739075352Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.739075352, -0.739075352}Solution
x = {50.739075352, -0.739075352}
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