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Simplifying x = -0.02x2 + 1.2x + 5.085 Reorder the terms: x = 5.085 + 1.2x + -0.02x2 Solving x = 5.085 + 1.2x + -0.02x2 Solving for variable 'x'. Reorder the terms: -5.085 + x + -1.2x + 0.02x2 = 5.085 + 1.2x + -0.02x2 + -5.085 + -1.2x + 0.02x2 Combine like terms: x + -1.2x = -0.2x -5.085 + -0.2x + 0.02x2 = 5.085 + 1.2x + -0.02x2 + -5.085 + -1.2x + 0.02x2 Reorder the terms: -5.085 + -0.2x + 0.02x2 = 5.085 + -5.085 + 1.2x + -1.2x + -0.02x2 + 0.02x2 Combine like terms: 5.085 + -5.085 = 0.000 -5.085 + -0.2x + 0.02x2 = 0.000 + 1.2x + -1.2x + -0.02x2 + 0.02x2 -5.085 + -0.2x + 0.02x2 = 1.2x + -1.2x + -0.02x2 + 0.02x2 Combine like terms: 1.2x + -1.2x = 0.0 -5.085 + -0.2x + 0.02x2 = 0.0 + -0.02x2 + 0.02x2 -5.085 + -0.2x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 -5.085 + -0.2x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -254.25 + -10x + x2 = 0 Move the constant term to the right: Add '254.25' to each side of the equation. -254.25 + -10x + 254.25 + x2 = 0 + 254.25 Reorder the terms: -254.25 + 254.25 + -10x + x2 = 0 + 254.25 Combine like terms: -254.25 + 254.25 = 0.00 0.00 + -10x + x2 = 0 + 254.25 -10x + x2 = 0 + 254.25 Combine like terms: 0 + 254.25 = 254.25 -10x + x2 = 254.25 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 254.25 + 25 Reorder the terms: 25 + -10x + x2 = 254.25 + 25 Combine like terms: 254.25 + 25 = 279.25 25 + -10x + x2 = 279.25 Factor a perfect square on the left side: (x + -5)(x + -5) = 279.25 Calculate the square root of the right side: 16.710774967 Break this problem into two subproblems by setting (x + -5) equal to 16.710774967 and -16.710774967.Subproblem 1
x + -5 = 16.710774967 Simplifying x + -5 = 16.710774967 Reorder the terms: -5 + x = 16.710774967 Solving -5 + x = 16.710774967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 16.710774967 + 5 Combine like terms: -5 + 5 = 0 0 + x = 16.710774967 + 5 x = 16.710774967 + 5 Combine like terms: 16.710774967 + 5 = 21.710774967 x = 21.710774967 Simplifying x = 21.710774967Subproblem 2
x + -5 = -16.710774967 Simplifying x + -5 = -16.710774967 Reorder the terms: -5 + x = -16.710774967 Solving -5 + x = -16.710774967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -16.710774967 + 5 Combine like terms: -5 + 5 = 0 0 + x = -16.710774967 + 5 x = -16.710774967 + 5 Combine like terms: -16.710774967 + 5 = -11.710774967 x = -11.710774967 Simplifying x = -11.710774967Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.710774967, -11.710774967}
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