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Simplifying 7x(-9x + -3) = 1 + -1(4x + -7) Reorder the terms: 7x(-3 + -9x) = 1 + -1(4x + -7) (-3 * 7x + -9x * 7x) = 1 + -1(4x + -7) (-21x + -63x2) = 1 + -1(4x + -7) Reorder the terms: -21x + -63x2 = 1 + -1(-7 + 4x) -21x + -63x2 = 1 + (-7 * -1 + 4x * -1) -21x + -63x2 = 1 + (7 + -4x) Combine like terms: 1 + 7 = 8 -21x + -63x2 = 8 + -4x Solving -21x + -63x2 = 8 + -4x Solving for variable 'x'. Reorder the terms: -8 + -21x + 4x + -63x2 = 8 + -4x + -8 + 4x Combine like terms: -21x + 4x = -17x -8 + -17x + -63x2 = 8 + -4x + -8 + 4x Reorder the terms: -8 + -17x + -63x2 = 8 + -8 + -4x + 4x Combine like terms: 8 + -8 = 0 -8 + -17x + -63x2 = 0 + -4x + 4x -8 + -17x + -63x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -8 + -17x + -63x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 17x + 63x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 17x + 63x2)' equal to zero and attempt to solve: Simplifying 8 + 17x + 63x2 = 0 Solving 8 + 17x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. 0.126984127 + 0.2698412698x + x2 = 0 Move the constant term to the right: Add '-0.126984127' to each side of the equation. 0.126984127 + 0.2698412698x + -0.126984127 + x2 = 0 + -0.126984127 Reorder the terms: 0.126984127 + -0.126984127 + 0.2698412698x + x2 = 0 + -0.126984127 Combine like terms: 0.126984127 + -0.126984127 = 0.000000000 0.000000000 + 0.2698412698x + x2 = 0 + -0.126984127 0.2698412698x + x2 = 0 + -0.126984127 Combine like terms: 0 + -0.126984127 = -0.126984127 0.2698412698x + x2 = -0.126984127 The x term is 0.2698412698x. Take half its coefficient (0.1349206349). Square it (0.01820357772) and add it to both sides. Add '0.01820357772' to each side of the equation. 0.2698412698x + 0.01820357772 + x2 = -0.126984127 + 0.01820357772 Reorder the terms: 0.01820357772 + 0.2698412698x + x2 = -0.126984127 + 0.01820357772 Combine like terms: -0.126984127 + 0.01820357772 = -0.10878054928 0.01820357772 + 0.2698412698x + x2 = -0.10878054928 Factor a perfect square on the left side: (x + 0.1349206349)(x + 0.1349206349) = -0.10878054928 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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