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Simplifying 1.5x2 + 2.5x + -1 = 128 Reorder the terms: -1 + 2.5x + 1.5x2 = 128 Solving -1 + 2.5x + 1.5x2 = 128 Solving for variable 'x'. Reorder the terms: -1 + -128 + 2.5x + 1.5x2 = 128 + -128 Combine like terms: -1 + -128 = -129 -129 + 2.5x + 1.5x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -129 + 2.5x + 1.5x2 = 0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -86 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '86' to each side of the equation. -86 + 1.666666667x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 1.666666667x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 1.666666667x + x2 = 0 + 86 1.666666667x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 1.666666667x + x2 = 86 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 86 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 86 + 0.6944444447 Combine like terms: 86 + 0.6944444447 = 86.6944444447 0.6944444447 + 1.666666667x + x2 = 86.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 86.6944444447 Calculate the square root of the right side: 9.310985149 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 9.310985149 and -9.310985149.Subproblem 1
x + 0.8333333335 = 9.310985149 Simplifying x + 0.8333333335 = 9.310985149 Reorder the terms: 0.8333333335 + x = 9.310985149 Solving 0.8333333335 + x = 9.310985149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 9.310985149 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 9.310985149 + -0.8333333335 x = 9.310985149 + -0.8333333335 Combine like terms: 9.310985149 + -0.8333333335 = 8.4776518155 x = 8.4776518155 Simplifying x = 8.4776518155Subproblem 2
x + 0.8333333335 = -9.310985149 Simplifying x + 0.8333333335 = -9.310985149 Reorder the terms: 0.8333333335 + x = -9.310985149 Solving 0.8333333335 + x = -9.310985149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -9.310985149 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -9.310985149 + -0.8333333335 x = -9.310985149 + -0.8333333335 Combine like terms: -9.310985149 + -0.8333333335 = -10.1443184825 x = -10.1443184825 Simplifying x = -10.1443184825Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.4776518155, -10.1443184825}
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