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Simplifying x = -0.2x2 + 8x + 9 Reorder the terms: x = 9 + 8x + -0.2x2 Solving x = 9 + 8x + -0.2x2 Solving for variable 'x'. Reorder the terms: -9 + x + -8x + 0.2x2 = 9 + 8x + -0.2x2 + -9 + -8x + 0.2x2 Combine like terms: x + -8x = -7x -9 + -7x + 0.2x2 = 9 + 8x + -0.2x2 + -9 + -8x + 0.2x2 Reorder the terms: -9 + -7x + 0.2x2 = 9 + -9 + 8x + -8x + -0.2x2 + 0.2x2 Combine like terms: 9 + -9 = 0 -9 + -7x + 0.2x2 = 0 + 8x + -8x + -0.2x2 + 0.2x2 -9 + -7x + 0.2x2 = 8x + -8x + -0.2x2 + 0.2x2 Combine like terms: 8x + -8x = 0 -9 + -7x + 0.2x2 = 0 + -0.2x2 + 0.2x2 -9 + -7x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 -9 + -7x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -45 + -35x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -35x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -35x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -35x + x2 = 0 + 45 -35x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -35x + x2 = 45 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = 45 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 45 + 306.25 Combine like terms: 45 + 306.25 = 351.25 306.25 + -35x + x2 = 351.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 351.25 Calculate the square root of the right side: 18.741664814 Break this problem into two subproblems by setting (x + -17.5) equal to 18.741664814 and -18.741664814.Subproblem 1
x + -17.5 = 18.741664814 Simplifying x + -17.5 = 18.741664814 Reorder the terms: -17.5 + x = 18.741664814 Solving -17.5 + x = 18.741664814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 18.741664814 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 18.741664814 + 17.5 x = 18.741664814 + 17.5 Combine like terms: 18.741664814 + 17.5 = 36.241664814 x = 36.241664814 Simplifying x = 36.241664814Subproblem 2
x + -17.5 = -18.741664814 Simplifying x + -17.5 = -18.741664814 Reorder the terms: -17.5 + x = -18.741664814 Solving -17.5 + x = -18.741664814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -18.741664814 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -18.741664814 + 17.5 x = -18.741664814 + 17.5 Combine like terms: -18.741664814 + 17.5 = -1.241664814 x = -1.241664814 Simplifying x = -1.241664814Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.241664814, -1.241664814}
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