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Simplifying 6(x + -6) + 6 = 8x(x + x) + -12 Reorder the terms: 6(-6 + x) + 6 = 8x(x + x) + -12 (-6 * 6 + x * 6) + 6 = 8x(x + x) + -12 (-36 + 6x) + 6 = 8x(x + x) + -12 Reorder the terms: -36 + 6 + 6x = 8x(x + x) + -12 Combine like terms: -36 + 6 = -30 -30 + 6x = 8x(x + x) + -12 Combine like terms: x + x = 2x -30 + 6x = 8x(2x) + -12 Remove parenthesis around (2x) -30 + 6x = 8x * 2x + -12 Reorder the terms for easier multiplication: -30 + 6x = 8 * 2x * x + -12 Multiply 8 * 2 -30 + 6x = 16x * x + -12 Multiply x * x -30 + 6x = 16x2 + -12 Reorder the terms: -30 + 6x = -12 + 16x2 Solving -30 + 6x = -12 + 16x2 Solving for variable 'x'. Reorder the terms: -30 + 12 + 6x + -16x2 = -12 + 16x2 + 12 + -16x2 Combine like terms: -30 + 12 = -18 -18 + 6x + -16x2 = -12 + 16x2 + 12 + -16x2 Reorder the terms: -18 + 6x + -16x2 = -12 + 12 + 16x2 + -16x2 Combine like terms: -12 + 12 = 0 -18 + 6x + -16x2 = 0 + 16x2 + -16x2 -18 + 6x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -18 + 6x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 3x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 3x + -8x2)' equal to zero and attempt to solve: Simplifying -9 + 3x + -8x2 = 0 Solving -9 + 3x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.125 + -0.375x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -0.375x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -0.375x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -0.375x + x2 = 0 + -1.125 -0.375x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -0.375x + x2 = -1.125 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = -1.125 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = -1.125 + 0.03515625 Combine like terms: -1.125 + 0.03515625 = -1.08984375 0.03515625 + -0.375x + x2 = -1.08984375 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = -1.08984375 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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