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Simplifying 0.08 = -0.0082x2 + 0.06x Reorder the terms: 0.08 = 0.06x + -0.0082x2 Solving 0.08 = 0.06x + -0.0082x2 Solving for variable 'x'. Reorder the terms: 0.08 + -0.06x + 0.0082x2 = 0.06x + -0.06x + -0.0082x2 + 0.0082x2 Combine like terms: 0.06x + -0.06x = 0.00 0.08 + -0.06x + 0.0082x2 = 0.00 + -0.0082x2 + 0.0082x2 0.08 + -0.06x + 0.0082x2 = -0.0082x2 + 0.0082x2 Combine like terms: -0.0082x2 + 0.0082x2 = 0.0000 0.08 + -0.06x + 0.0082x2 = 0.0000 Begin completing the square. Divide all terms by 0.0082 the coefficient of the squared term: Divide each side by '0.0082'. 9.756097561 + -7.317073171x + x2 = 0 Move the constant term to the right: Add '-9.756097561' to each side of the equation. 9.756097561 + -7.317073171x + -9.756097561 + x2 = 0 + -9.756097561 Reorder the terms: 9.756097561 + -9.756097561 + -7.317073171x + x2 = 0 + -9.756097561 Combine like terms: 9.756097561 + -9.756097561 = 0.000000000 0.000000000 + -7.317073171x + x2 = 0 + -9.756097561 -7.317073171x + x2 = 0 + -9.756097561 Combine like terms: 0 + -9.756097561 = -9.756097561 -7.317073171x + x2 = -9.756097561 The x term is -7.317073171x. Take half its coefficient (-3.658536586). Square it (13.38488995) and add it to both sides. Add '13.38488995' to each side of the equation. -7.317073171x + 13.38488995 + x2 = -9.756097561 + 13.38488995 Reorder the terms: 13.38488995 + -7.317073171x + x2 = -9.756097561 + 13.38488995 Combine like terms: -9.756097561 + 13.38488995 = 3.628792389 13.38488995 + -7.317073171x + x2 = 3.628792389 Factor a perfect square on the left side: (x + -3.658536586)(x + -3.658536586) = 3.628792389 Calculate the square root of the right side: 1.904938946 Break this problem into two subproblems by setting (x + -3.658536586) equal to 1.904938946 and -1.904938946.Subproblem 1
x + -3.658536586 = 1.904938946 Simplifying x + -3.658536586 = 1.904938946 Reorder the terms: -3.658536586 + x = 1.904938946 Solving -3.658536586 + x = 1.904938946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.658536586' to each side of the equation. -3.658536586 + 3.658536586 + x = 1.904938946 + 3.658536586 Combine like terms: -3.658536586 + 3.658536586 = 0.000000000 0.000000000 + x = 1.904938946 + 3.658536586 x = 1.904938946 + 3.658536586 Combine like terms: 1.904938946 + 3.658536586 = 5.563475532 x = 5.563475532 Simplifying x = 5.563475532Subproblem 2
x + -3.658536586 = -1.904938946 Simplifying x + -3.658536586 = -1.904938946 Reorder the terms: -3.658536586 + x = -1.904938946 Solving -3.658536586 + x = -1.904938946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.658536586' to each side of the equation. -3.658536586 + 3.658536586 + x = -1.904938946 + 3.658536586 Combine like terms: -3.658536586 + 3.658536586 = 0.000000000 0.000000000 + x = -1.904938946 + 3.658536586 x = -1.904938946 + 3.658536586 Combine like terms: -1.904938946 + 3.658536586 = 1.75359764 x = 1.75359764 Simplifying x = 1.75359764Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.563475532, 1.75359764}
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