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Simplifying -7x + 18 + -7(x + -3) = 4x + -1(6x + -6) * 8x + 9 Reorder the terms: -7x + 18 + -7(-3 + x) = 4x + -1(6x + -6) * 8x + 9 -7x + 18 + (-3 * -7 + x * -7) = 4x + -1(6x + -6) * 8x + 9 -7x + 18 + (21 + -7x) = 4x + -1(6x + -6) * 8x + 9 Reorder the terms: 18 + 21 + -7x + -7x = 4x + -1(6x + -6) * 8x + 9 Combine like terms: 18 + 21 = 39 39 + -7x + -7x = 4x + -1(6x + -6) * 8x + 9 Combine like terms: -7x + -7x = -14x 39 + -14x = 4x + -1(6x + -6) * 8x + 9 Reorder the terms: 39 + -14x = 4x + -1(-6 + 6x) * 8x + 9 Reorder the terms for easier multiplication: 39 + -14x = 4x + -1 * 8x(-6 + 6x) + 9 Multiply -1 * 8 39 + -14x = 4x + -8x(-6 + 6x) + 9 39 + -14x = 4x + (-6 * -8x + 6x * -8x) + 9 39 + -14x = 4x + (48x + -48x2) + 9 Reorder the terms: 39 + -14x = 9 + 4x + 48x + -48x2 Combine like terms: 4x + 48x = 52x 39 + -14x = 9 + 52x + -48x2 Solving 39 + -14x = 9 + 52x + -48x2 Solving for variable 'x'. Reorder the terms: 39 + -9 + -14x + -52x + 48x2 = 9 + 52x + -48x2 + -9 + -52x + 48x2 Combine like terms: 39 + -9 = 30 30 + -14x + -52x + 48x2 = 9 + 52x + -48x2 + -9 + -52x + 48x2 Combine like terms: -14x + -52x = -66x 30 + -66x + 48x2 = 9 + 52x + -48x2 + -9 + -52x + 48x2 Reorder the terms: 30 + -66x + 48x2 = 9 + -9 + 52x + -52x + -48x2 + 48x2 Combine like terms: 9 + -9 = 0 30 + -66x + 48x2 = 0 + 52x + -52x + -48x2 + 48x2 30 + -66x + 48x2 = 52x + -52x + -48x2 + 48x2 Combine like terms: 52x + -52x = 0 30 + -66x + 48x2 = 0 + -48x2 + 48x2 30 + -66x + 48x2 = -48x2 + 48x2 Combine like terms: -48x2 + 48x2 = 0 30 + -66x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(5 + -11x + 8x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + -11x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + -11x + 8x2 = 0 Solving 5 + -11x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -1.375x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -1.375x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -1.375x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -1.375x + x2 = 0 + -0.625 -1.375x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -1.375x + x2 = -0.625 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = -0.625 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = -0.625 + 0.47265625 Combine like terms: -0.625 + 0.47265625 = -0.15234375 0.47265625 + -1.375x + x2 = -0.15234375 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = -0.15234375 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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