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Simplifying 0 = -0.00625x2 + 0.15x + 2.5 Reorder the terms: 0 = 2.5 + 0.15x + -0.00625x2 Solving 0 = 2.5 + 0.15x + -0.00625x2 Solving for variable 'x'. Combine like terms: 0 + -2.5 = -2.5 -2.5 + -0.15x + 0.00625x2 = 2.5 + 0.15x + -0.00625x2 + -2.5 + -0.15x + 0.00625x2 Reorder the terms: -2.5 + -0.15x + 0.00625x2 = 2.5 + -2.5 + 0.15x + -0.15x + -0.00625x2 + 0.00625x2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + -0.15x + 0.00625x2 = 0.0 + 0.15x + -0.15x + -0.00625x2 + 0.00625x2 -2.5 + -0.15x + 0.00625x2 = 0.15x + -0.15x + -0.00625x2 + 0.00625x2 Combine like terms: 0.15x + -0.15x = 0.00 -2.5 + -0.15x + 0.00625x2 = 0.00 + -0.00625x2 + 0.00625x2 -2.5 + -0.15x + 0.00625x2 = -0.00625x2 + 0.00625x2 Combine like terms: -0.00625x2 + 0.00625x2 = 0.00000 -2.5 + -0.15x + 0.00625x2 = 0.00000 Begin completing the square. Divide all terms by 0.00625 the coefficient of the squared term: Divide each side by '0.00625'. -400 + -24x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -24x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -24x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -24x + x2 = 0 + 400 -24x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -24x + x2 = 400 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 400 + 144 Reorder the terms: 144 + -24x + x2 = 400 + 144 Combine like terms: 400 + 144 = 544 144 + -24x + x2 = 544 Factor a perfect square on the left side: (x + -12)(x + -12) = 544 Calculate the square root of the right side: 23.323807579 Break this problem into two subproblems by setting (x + -12) equal to 23.323807579 and -23.323807579.Subproblem 1
x + -12 = 23.323807579 Simplifying x + -12 = 23.323807579 Reorder the terms: -12 + x = 23.323807579 Solving -12 + x = 23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 23.323807579 + 12 Combine like terms: -12 + 12 = 0 0 + x = 23.323807579 + 12 x = 23.323807579 + 12 Combine like terms: 23.323807579 + 12 = 35.323807579 x = 35.323807579 Simplifying x = 35.323807579Subproblem 2
x + -12 = -23.323807579 Simplifying x + -12 = -23.323807579 Reorder the terms: -12 + x = -23.323807579 Solving -12 + x = -23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -23.323807579 + 12 Combine like terms: -12 + 12 = 0 0 + x = -23.323807579 + 12 x = -23.323807579 + 12 Combine like terms: -23.323807579 + 12 = -11.323807579 x = -11.323807579 Simplifying x = -11.323807579Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.323807579, -11.323807579}
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