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Simplifying 0 = -2x2 + 12x + -15 Reorder the terms: 0 = -15 + 12x + -2x2 Solving 0 = -15 + 12x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 15 = 15 15 + -12x + 2x2 = -15 + 12x + -2x2 + 15 + -12x + 2x2 Reorder the terms: 15 + -12x + 2x2 = -15 + 15 + 12x + -12x + -2x2 + 2x2 Combine like terms: -15 + 15 = 0 15 + -12x + 2x2 = 0 + 12x + -12x + -2x2 + 2x2 15 + -12x + 2x2 = 12x + -12x + -2x2 + 2x2 Combine like terms: 12x + -12x = 0 15 + -12x + 2x2 = 0 + -2x2 + 2x2 15 + -12x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 15 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -6x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -6x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -6x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -6x + x2 = 0 + -7.5 -6x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -6x + x2 = -7.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7.5 + 9 Reorder the terms: 9 + -6x + x2 = -7.5 + 9 Combine like terms: -7.5 + 9 = 1.5 9 + -6x + x2 = 1.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -3) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -3 = 1.224744871 Simplifying x + -3 = 1.224744871 Reorder the terms: -3 + x = 1.224744871 Solving -3 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.224744871 + 3 x = 1.224744871 + 3 Combine like terms: 1.224744871 + 3 = 4.224744871 x = 4.224744871 Simplifying x = 4.224744871Subproblem 2
x + -3 = -1.224744871 Simplifying x + -3 = -1.224744871 Reorder the terms: -3 + x = -1.224744871 Solving -3 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.224744871 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.224744871 + 3 x = -1.224744871 + 3 Combine like terms: -1.224744871 + 3 = 1.775255129 x = 1.775255129 Simplifying x = 1.775255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.224744871, 1.775255129}
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