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Simplifying -0.01x2 + 24x + 8.96 = 0 Reorder the terms: 8.96 + 24x + -0.01x2 = 0 Solving 8.96 + 24x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -896 + -2400x + x2 = 0 Move the constant term to the right: Add '896' to each side of the equation. -896 + -2400x + 896 + x2 = 0 + 896 Reorder the terms: -896 + 896 + -2400x + x2 = 0 + 896 Combine like terms: -896 + 896 = 0 0 + -2400x + x2 = 0 + 896 -2400x + x2 = 0 + 896 Combine like terms: 0 + 896 = 896 -2400x + x2 = 896 The x term is -2400x. Take half its coefficient (-1200). Square it (1440000) and add it to both sides. Add '1440000' to each side of the equation. -2400x + 1440000 + x2 = 896 + 1440000 Reorder the terms: 1440000 + -2400x + x2 = 896 + 1440000 Combine like terms: 896 + 1440000 = 1440896 1440000 + -2400x + x2 = 1440896 Factor a perfect square on the left side: (x + -1200)(x + -1200) = 1440896 Calculate the square root of the right side: 1200.373275277 Break this problem into two subproblems by setting (x + -1200) equal to 1200.373275277 and -1200.373275277.Subproblem 1
x + -1200 = 1200.373275277 Simplifying x + -1200 = 1200.373275277 Reorder the terms: -1200 + x = 1200.373275277 Solving -1200 + x = 1200.373275277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1200' to each side of the equation. -1200 + 1200 + x = 1200.373275277 + 1200 Combine like terms: -1200 + 1200 = 0 0 + x = 1200.373275277 + 1200 x = 1200.373275277 + 1200 Combine like terms: 1200.373275277 + 1200 = 2400.373275277 x = 2400.373275277 Simplifying x = 2400.373275277Subproblem 2
x + -1200 = -1200.373275277 Simplifying x + -1200 = -1200.373275277 Reorder the terms: -1200 + x = -1200.373275277 Solving -1200 + x = -1200.373275277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1200' to each side of the equation. -1200 + 1200 + x = -1200.373275277 + 1200 Combine like terms: -1200 + 1200 = 0 0 + x = -1200.373275277 + 1200 x = -1200.373275277 + 1200 Combine like terms: -1200.373275277 + 1200 = -0.373275277 x = -0.373275277 Simplifying x = -0.373275277Solution
The solution to the problem is based on the solutions from the subproblems. x = {2400.373275277, -0.373275277}
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