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Simplifying 4x2 + -2x = 200 Reorder the terms: -2x + 4x2 = 200 Solving -2x + 4x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -2x + 4x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -100 + -1x + 2x2 = 0 Solving -100 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + -0.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -0.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -0.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -0.5x + x2 = 0 + 50 -0.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -0.5x + x2 = 50 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 50 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 50 + 0.0625 Combine like terms: 50 + 0.0625 = 50.0625 0.0625 + -0.5x + x2 = 50.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 50.0625 Calculate the square root of the right side: 7.075485849 Break this problem into two subproblems by setting (x + -0.25) equal to 7.075485849 and -7.075485849.Subproblem 1
x + -0.25 = 7.075485849 Simplifying x + -0.25 = 7.075485849 Reorder the terms: -0.25 + x = 7.075485849 Solving -0.25 + x = 7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 7.075485849 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 7.075485849 + 0.25 x = 7.075485849 + 0.25 Combine like terms: 7.075485849 + 0.25 = 7.325485849 x = 7.325485849 Simplifying x = 7.325485849Subproblem 2
x + -0.25 = -7.075485849 Simplifying x + -0.25 = -7.075485849 Reorder the terms: -0.25 + x = -7.075485849 Solving -0.25 + x = -7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -7.075485849 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -7.075485849 + 0.25 x = -7.075485849 + 0.25 Combine like terms: -7.075485849 + 0.25 = -6.825485849 x = -6.825485849 Simplifying x = -6.825485849Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.325485849, -6.825485849}Solution
x = {7.325485849, -6.825485849}
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