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Simplifying x + -0.2x + 0.06x(x + -0.2x) = 66.91 Combine like terms: x + -0.2x = 0.8x x + -0.2x + 0.06x(0.8x) = 66.91 Remove parenthesis around (0.8x) x + -0.2x + 0.06x * 0.8x = 66.91 Reorder the terms for easier multiplication: x + -0.2x + 0.06 * 0.8x * x = 66.91 Multiply 0.06 * 0.8 x + -0.2x + 0.048x * x = 66.91 Multiply x * x x + -0.2x + 0.048x2 = 66.91 Combine like terms: x + -0.2x = 0.8x 0.8x + 0.048x2 = 66.91 Solving 0.8x + 0.048x2 = 66.91 Solving for variable 'x'. Reorder the terms: -66.91 + 0.8x + 0.048x2 = 66.91 + -66.91 Combine like terms: 66.91 + -66.91 = 0.00 -66.91 + 0.8x + 0.048x2 = 0.00 Begin completing the square. Divide all terms by 0.048 the coefficient of the squared term: Divide each side by '0.048'. -1393.958333 + 16.66666667x + x2 = 0 Move the constant term to the right: Add '1393.958333' to each side of the equation. -1393.958333 + 16.66666667x + 1393.958333 + x2 = 0 + 1393.958333 Reorder the terms: -1393.958333 + 1393.958333 + 16.66666667x + x2 = 0 + 1393.958333 Combine like terms: -1393.958333 + 1393.958333 = 0.000000 0.000000 + 16.66666667x + x2 = 0 + 1393.958333 16.66666667x + x2 = 0 + 1393.958333 Combine like terms: 0 + 1393.958333 = 1393.958333 16.66666667x + x2 = 1393.958333 The x term is 16.66666667x. Take half its coefficient (8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. 16.66666667x + 69.44444447 + x2 = 1393.958333 + 69.44444447 Reorder the terms: 69.44444447 + 16.66666667x + x2 = 1393.958333 + 69.44444447 Combine like terms: 1393.958333 + 69.44444447 = 1463.40277747 69.44444447 + 16.66666667x + x2 = 1463.40277747 Factor a perfect square on the left side: (x + 8.333333335)(x + 8.333333335) = 1463.40277747 Calculate the square root of the right side: 38.254447813 Break this problem into two subproblems by setting (x + 8.333333335) equal to 38.254447813 and -38.254447813.Subproblem 1
x + 8.333333335 = 38.254447813 Simplifying x + 8.333333335 = 38.254447813 Reorder the terms: 8.333333335 + x = 38.254447813 Solving 8.333333335 + x = 38.254447813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.333333335' to each side of the equation. 8.333333335 + -8.333333335 + x = 38.254447813 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + x = 38.254447813 + -8.333333335 x = 38.254447813 + -8.333333335 Combine like terms: 38.254447813 + -8.333333335 = 29.921114478 x = 29.921114478 Simplifying x = 29.921114478Subproblem 2
x + 8.333333335 = -38.254447813 Simplifying x + 8.333333335 = -38.254447813 Reorder the terms: 8.333333335 + x = -38.254447813 Solving 8.333333335 + x = -38.254447813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.333333335' to each side of the equation. 8.333333335 + -8.333333335 + x = -38.254447813 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + x = -38.254447813 + -8.333333335 x = -38.254447813 + -8.333333335 Combine like terms: -38.254447813 + -8.333333335 = -46.587781148 x = -46.587781148 Simplifying x = -46.587781148Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.921114478, -46.587781148}
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