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Simplifying x = 0.5(0.25x2 + 4.6225 + -2.15x) Reorder the terms: x = 0.5(4.6225 + -2.15x + 0.25x2) x = (4.6225 * 0.5 + -2.15x * 0.5 + 0.25x2 * 0.5) x = (2.31125 + -1.075x + 0.125x2) Solving x = 2.31125 + -1.075x + 0.125x2 Solving for variable 'x'. Reorder the terms: -2.31125 + x + 1.075x + -0.125x2 = 2.31125 + -1.075x + 0.125x2 + -2.31125 + 1.075x + -0.125x2 Combine like terms: x + 1.075x = 2.075x -2.31125 + 2.075x + -0.125x2 = 2.31125 + -1.075x + 0.125x2 + -2.31125 + 1.075x + -0.125x2 Reorder the terms: -2.31125 + 2.075x + -0.125x2 = 2.31125 + -2.31125 + -1.075x + 1.075x + 0.125x2 + -0.125x2 Combine like terms: 2.31125 + -2.31125 = 0.00000 -2.31125 + 2.075x + -0.125x2 = 0.00000 + -1.075x + 1.075x + 0.125x2 + -0.125x2 -2.31125 + 2.075x + -0.125x2 = -1.075x + 1.075x + 0.125x2 + -0.125x2 Combine like terms: -1.075x + 1.075x = 0.000 -2.31125 + 2.075x + -0.125x2 = 0.000 + 0.125x2 + -0.125x2 -2.31125 + 2.075x + -0.125x2 = 0.125x2 + -0.125x2 Combine like terms: 0.125x2 + -0.125x2 = 0.000 -2.31125 + 2.075x + -0.125x2 = 0.000 Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. 18.49 + -16.6x + x2 = 0 Move the constant term to the right: Add '-18.49' to each side of the equation. 18.49 + -16.6x + -18.49 + x2 = 0 + -18.49 Reorder the terms: 18.49 + -18.49 + -16.6x + x2 = 0 + -18.49 Combine like terms: 18.49 + -18.49 = 0.00 0.00 + -16.6x + x2 = 0 + -18.49 -16.6x + x2 = 0 + -18.49 Combine like terms: 0 + -18.49 = -18.49 -16.6x + x2 = -18.49 The x term is -16.6x. Take half its coefficient (-8.3). Square it (68.89) and add it to both sides. Add '68.89' to each side of the equation. -16.6x + 68.89 + x2 = -18.49 + 68.89 Reorder the terms: 68.89 + -16.6x + x2 = -18.49 + 68.89 Combine like terms: -18.49 + 68.89 = 50.4 68.89 + -16.6x + x2 = 50.4 Factor a perfect square on the left side: (x + -8.3)(x + -8.3) = 50.4 Calculate the square root of the right side: 7.09929574 Break this problem into two subproblems by setting (x + -8.3) equal to 7.09929574 and -7.09929574.Subproblem 1
x + -8.3 = 7.09929574 Simplifying x + -8.3 = 7.09929574 Reorder the terms: -8.3 + x = 7.09929574 Solving -8.3 + x = 7.09929574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.3' to each side of the equation. -8.3 + 8.3 + x = 7.09929574 + 8.3 Combine like terms: -8.3 + 8.3 = 0.0 0.0 + x = 7.09929574 + 8.3 x = 7.09929574 + 8.3 Combine like terms: 7.09929574 + 8.3 = 15.39929574 x = 15.39929574 Simplifying x = 15.39929574Subproblem 2
x + -8.3 = -7.09929574 Simplifying x + -8.3 = -7.09929574 Reorder the terms: -8.3 + x = -7.09929574 Solving -8.3 + x = -7.09929574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.3' to each side of the equation. -8.3 + 8.3 + x = -7.09929574 + 8.3 Combine like terms: -8.3 + 8.3 = 0.0 0.0 + x = -7.09929574 + 8.3 x = -7.09929574 + 8.3 Combine like terms: -7.09929574 + 8.3 = 1.20070426 x = 1.20070426 Simplifying x = 1.20070426Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.39929574, 1.20070426}
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