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Simplifying 300 = -16x2 + 200x Reorder the terms: 300 = 200x + -16x2 Solving 300 = 200x + -16x2 Solving for variable 'x'. Reorder the terms: 300 + -200x + 16x2 = 200x + -200x + -16x2 + 16x2 Combine like terms: 200x + -200x = 0 300 + -200x + 16x2 = 0 + -16x2 + 16x2 300 + -200x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 300 + -200x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(75 + -50x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(75 + -50x + 4x2)' equal to zero and attempt to solve: Simplifying 75 + -50x + 4x2 = 0 Solving 75 + -50x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 18.75 + -12.5x + x2 = 0 Move the constant term to the right: Add '-18.75' to each side of the equation. 18.75 + -12.5x + -18.75 + x2 = 0 + -18.75 Reorder the terms: 18.75 + -18.75 + -12.5x + x2 = 0 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + -12.5x + x2 = 0 + -18.75 -12.5x + x2 = 0 + -18.75 Combine like terms: 0 + -18.75 = -18.75 -12.5x + x2 = -18.75 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -18.75 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -18.75 + 39.0625 Combine like terms: -18.75 + 39.0625 = 20.3125 39.0625 + -12.5x + x2 = 20.3125 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 20.3125 Calculate the square root of the right side: 4.506939094 Break this problem into two subproblems by setting (x + -6.25) equal to 4.506939094 and -4.506939094.Subproblem 1
x + -6.25 = 4.506939094 Simplifying x + -6.25 = 4.506939094 Reorder the terms: -6.25 + x = 4.506939094 Solving -6.25 + x = 4.506939094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 4.506939094 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 4.506939094 + 6.25 x = 4.506939094 + 6.25 Combine like terms: 4.506939094 + 6.25 = 10.756939094 x = 10.756939094 Simplifying x = 10.756939094Subproblem 2
x + -6.25 = -4.506939094 Simplifying x + -6.25 = -4.506939094 Reorder the terms: -6.25 + x = -4.506939094 Solving -6.25 + x = -4.506939094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -4.506939094 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -4.506939094 + 6.25 x = -4.506939094 + 6.25 Combine like terms: -4.506939094 + 6.25 = 1.743060906 x = 1.743060906 Simplifying x = 1.743060906Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.756939094, 1.743060906}Solution
x = {10.756939094, 1.743060906}
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