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Simplifying (6x + -9)(6x + -9) = 36x + -81 Reorder the terms: (-9 + 6x)(6x + -9) = 36x + -81 Reorder the terms: (-9 + 6x)(-9 + 6x) = 36x + -81 Multiply (-9 + 6x) * (-9 + 6x) (-9(-9 + 6x) + 6x * (-9 + 6x)) = 36x + -81 ((-9 * -9 + 6x * -9) + 6x * (-9 + 6x)) = 36x + -81 ((81 + -54x) + 6x * (-9 + 6x)) = 36x + -81 (81 + -54x + (-9 * 6x + 6x * 6x)) = 36x + -81 (81 + -54x + (-54x + 36x2)) = 36x + -81 Combine like terms: -54x + -54x = -108x (81 + -108x + 36x2) = 36x + -81 Reorder the terms: 81 + -108x + 36x2 = -81 + 36x Solving 81 + -108x + 36x2 = -81 + 36x Solving for variable 'x'. Reorder the terms: 81 + 81 + -108x + -36x + 36x2 = -81 + 36x + 81 + -36x Combine like terms: 81 + 81 = 162 162 + -108x + -36x + 36x2 = -81 + 36x + 81 + -36x Combine like terms: -108x + -36x = -144x 162 + -144x + 36x2 = -81 + 36x + 81 + -36x Reorder the terms: 162 + -144x + 36x2 = -81 + 81 + 36x + -36x Combine like terms: -81 + 81 = 0 162 + -144x + 36x2 = 0 + 36x + -36x 162 + -144x + 36x2 = 36x + -36x Combine like terms: 36x + -36x = 0 162 + -144x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '18'. 18(9 + -8x + 2x2) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(9 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -8x + 2x2 = 0 Solving 9 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -4x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -4x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -4x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -4x + x2 = 0 + -4.5 -4x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -4x + x2 = -4.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -4.5 + 4 Reorder the terms: 4 + -4x + x2 = -4.5 + 4 Combine like terms: -4.5 + 4 = -0.5 4 + -4x + x2 = -0.5 Factor a perfect square on the left side: (x + -2)(x + -2) = -0.5 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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