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Simplifying 3 + -1(x2 + -2x + 1) = 16x2 + 40x + 25 Reorder the terms: 3 + -1(1 + -2x + x2) = 16x2 + 40x + 25 3 + (1 * -1 + -2x * -1 + x2 * -1) = 16x2 + 40x + 25 3 + (-1 + 2x + -1x2) = 16x2 + 40x + 25 Combine like terms: 3 + -1 = 2 2 + 2x + -1x2 = 16x2 + 40x + 25 Reorder the terms: 2 + 2x + -1x2 = 25 + 40x + 16x2 Solving 2 + 2x + -1x2 = 25 + 40x + 16x2 Solving for variable 'x'. Reorder the terms: 2 + -25 + 2x + -40x + -1x2 + -16x2 = 25 + 40x + 16x2 + -25 + -40x + -16x2 Combine like terms: 2 + -25 = -23 -23 + 2x + -40x + -1x2 + -16x2 = 25 + 40x + 16x2 + -25 + -40x + -16x2 Combine like terms: 2x + -40x = -38x -23 + -38x + -1x2 + -16x2 = 25 + 40x + 16x2 + -25 + -40x + -16x2 Combine like terms: -1x2 + -16x2 = -17x2 -23 + -38x + -17x2 = 25 + 40x + 16x2 + -25 + -40x + -16x2 Reorder the terms: -23 + -38x + -17x2 = 25 + -25 + 40x + -40x + 16x2 + -16x2 Combine like terms: 25 + -25 = 0 -23 + -38x + -17x2 = 0 + 40x + -40x + 16x2 + -16x2 -23 + -38x + -17x2 = 40x + -40x + 16x2 + -16x2 Combine like terms: 40x + -40x = 0 -23 + -38x + -17x2 = 0 + 16x2 + -16x2 -23 + -38x + -17x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -23 + -38x + -17x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(23 + 38x + 17x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(23 + 38x + 17x2)' equal to zero and attempt to solve: Simplifying 23 + 38x + 17x2 = 0 Solving 23 + 38x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 1.352941176 + 2.235294118x + x2 = 0 Move the constant term to the right: Add '-1.352941176' to each side of the equation. 1.352941176 + 2.235294118x + -1.352941176 + x2 = 0 + -1.352941176 Reorder the terms: 1.352941176 + -1.352941176 + 2.235294118x + x2 = 0 + -1.352941176 Combine like terms: 1.352941176 + -1.352941176 = 0.000000000 0.000000000 + 2.235294118x + x2 = 0 + -1.352941176 2.235294118x + x2 = 0 + -1.352941176 Combine like terms: 0 + -1.352941176 = -1.352941176 2.235294118x + x2 = -1.352941176 The x term is 2.235294118x. Take half its coefficient (1.117647059). Square it (1.249134948) and add it to both sides. Add '1.249134948' to each side of the equation. 2.235294118x + 1.249134948 + x2 = -1.352941176 + 1.249134948 Reorder the terms: 1.249134948 + 2.235294118x + x2 = -1.352941176 + 1.249134948 Combine like terms: -1.352941176 + 1.249134948 = -0.103806228 1.249134948 + 2.235294118x + x2 = -0.103806228 Factor a perfect square on the left side: (x + 1.117647059)(x + 1.117647059) = -0.103806228 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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