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Simplifying 4x2 + 150x = 200 Reorder the terms: 150x + 4x2 = 200 Solving 150x + 4x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 150x + 4x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 150x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + 75x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + 75x + 2x2)' equal to zero and attempt to solve: Simplifying -100 + 75x + 2x2 = 0 Solving -100 + 75x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + 37.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 37.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 37.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 37.5x + x2 = 0 + 50 37.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 37.5x + x2 = 50 The x term is 37.5x. Take half its coefficient (18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. 37.5x + 351.5625 + x2 = 50 + 351.5625 Reorder the terms: 351.5625 + 37.5x + x2 = 50 + 351.5625 Combine like terms: 50 + 351.5625 = 401.5625 351.5625 + 37.5x + x2 = 401.5625 Factor a perfect square on the left side: (x + 18.75)(x + 18.75) = 401.5625 Calculate the square root of the right side: 20.039024427 Break this problem into two subproblems by setting (x + 18.75) equal to 20.039024427 and -20.039024427.Subproblem 1
x + 18.75 = 20.039024427 Simplifying x + 18.75 = 20.039024427 Reorder the terms: 18.75 + x = 20.039024427 Solving 18.75 + x = 20.039024427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 20.039024427 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 20.039024427 + -18.75 x = 20.039024427 + -18.75 Combine like terms: 20.039024427 + -18.75 = 1.289024427 x = 1.289024427 Simplifying x = 1.289024427Subproblem 2
x + 18.75 = -20.039024427 Simplifying x + 18.75 = -20.039024427 Reorder the terms: 18.75 + x = -20.039024427 Solving 18.75 + x = -20.039024427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -20.039024427 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -20.039024427 + -18.75 x = -20.039024427 + -18.75 Combine like terms: -20.039024427 + -18.75 = -38.789024427 x = -38.789024427 Simplifying x = -38.789024427Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.289024427, -38.789024427}Solution
x = {1.289024427, -38.789024427}
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