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Simplifying 200 = -16x2 + 150x Reorder the terms: 200 = 150x + -16x2 Solving 200 = 150x + -16x2 Solving for variable 'x'. Reorder the terms: 200 + -150x + 16x2 = 150x + -150x + -16x2 + 16x2 Combine like terms: 150x + -150x = 0 200 + -150x + 16x2 = 0 + -16x2 + 16x2 200 + -150x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 200 + -150x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + -75x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + -75x + 8x2)' equal to zero and attempt to solve: Simplifying 100 + -75x + 8x2 = 0 Solving 100 + -75x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 12.5 + -9.375x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -9.375x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -9.375x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -9.375x + x2 = 0 + -12.5 -9.375x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -9.375x + x2 = -12.5 The x term is -9.375x. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375x + 21.97265625 + x2 = -12.5 + 21.97265625 Reorder the terms: 21.97265625 + -9.375x + x2 = -12.5 + 21.97265625 Combine like terms: -12.5 + 21.97265625 = 9.47265625 21.97265625 + -9.375x + x2 = 9.47265625 Factor a perfect square on the left side: (x + -4.6875)(x + -4.6875) = 9.47265625 Calculate the square root of the right side: 3.077768063 Break this problem into two subproblems by setting (x + -4.6875) equal to 3.077768063 and -3.077768063.Subproblem 1
x + -4.6875 = 3.077768063 Simplifying x + -4.6875 = 3.077768063 Reorder the terms: -4.6875 + x = 3.077768063 Solving -4.6875 + x = 3.077768063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = 3.077768063 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = 3.077768063 + 4.6875 x = 3.077768063 + 4.6875 Combine like terms: 3.077768063 + 4.6875 = 7.765268063 x = 7.765268063 Simplifying x = 7.765268063Subproblem 2
x + -4.6875 = -3.077768063 Simplifying x + -4.6875 = -3.077768063 Reorder the terms: -4.6875 + x = -3.077768063 Solving -4.6875 + x = -3.077768063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = -3.077768063 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = -3.077768063 + 4.6875 x = -3.077768063 + 4.6875 Combine like terms: -3.077768063 + 4.6875 = 1.609731937 x = 1.609731937 Simplifying x = 1.609731937Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.765268063, 1.609731937}Solution
x = {7.765268063, 1.609731937}
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