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Simplifying 8 = 120 + 2x + -0.5x2 Solving 8 = 120 + 2x + -0.5x2 Solving for variable 'x'. Combine like terms: 8 + -120 = -112 -112 + -2x + 0.5x2 = 120 + 2x + -0.5x2 + -120 + -2x + 0.5x2 Reorder the terms: -112 + -2x + 0.5x2 = 120 + -120 + 2x + -2x + -0.5x2 + 0.5x2 Combine like terms: 120 + -120 = 0 -112 + -2x + 0.5x2 = 0 + 2x + -2x + -0.5x2 + 0.5x2 -112 + -2x + 0.5x2 = 2x + -2x + -0.5x2 + 0.5x2 Combine like terms: 2x + -2x = 0 -112 + -2x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -112 + -2x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -112 + -2x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -224 + -4x + x2 = 0 Move the constant term to the right: Add '224' to each side of the equation. -224 + -4x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + -4x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + -4x + x2 = 0 + 224 -4x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 -4x + x2 = 224 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 224 + 4 Reorder the terms: 4 + -4x + x2 = 224 + 4 Combine like terms: 224 + 4 = 228 4 + -4x + x2 = 228 Factor a perfect square on the left side: (x + -2)(x + -2) = 228 Calculate the square root of the right side: 15.099668871 Break this problem into two subproblems by setting (x + -2) equal to 15.099668871 and -15.099668871.Subproblem 1
x + -2 = 15.099668871 Simplifying x + -2 = 15.099668871 Reorder the terms: -2 + x = 15.099668871 Solving -2 + x = 15.099668871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 15.099668871 + 2 Combine like terms: -2 + 2 = 0 0 + x = 15.099668871 + 2 x = 15.099668871 + 2 Combine like terms: 15.099668871 + 2 = 17.099668871 x = 17.099668871 Simplifying x = 17.099668871Subproblem 2
x + -2 = -15.099668871 Simplifying x + -2 = -15.099668871 Reorder the terms: -2 + x = -15.099668871 Solving -2 + x = -15.099668871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -15.099668871 + 2 Combine like terms: -2 + 2 = 0 0 + x = -15.099668871 + 2 x = -15.099668871 + 2 Combine like terms: -15.099668871 + 2 = -13.099668871 x = -13.099668871 Simplifying x = -13.099668871Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.099668871, -13.099668871}
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