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Simplifying (x + 9)(x + 9) + (2x + -9)(2x + -9) = x2 Reorder the terms: (9 + x)(x + 9) + (2x + -9)(2x + -9) = x2 Reorder the terms: (9 + x)(9 + x) + (2x + -9)(2x + -9) = x2 Multiply (9 + x) * (9 + x) (9(9 + x) + x(9 + x)) + (2x + -9)(2x + -9) = x2 ((9 * 9 + x * 9) + x(9 + x)) + (2x + -9)(2x + -9) = x2 ((81 + 9x) + x(9 + x)) + (2x + -9)(2x + -9) = x2 (81 + 9x + (9 * x + x * x)) + (2x + -9)(2x + -9) = x2 (81 + 9x + (9x + x2)) + (2x + -9)(2x + -9) = x2 Combine like terms: 9x + 9x = 18x (81 + 18x + x2) + (2x + -9)(2x + -9) = x2 Reorder the terms: 81 + 18x + x2 + (-9 + 2x)(2x + -9) = x2 Reorder the terms: 81 + 18x + x2 + (-9 + 2x)(-9 + 2x) = x2 Multiply (-9 + 2x) * (-9 + 2x) 81 + 18x + x2 + (-9(-9 + 2x) + 2x * (-9 + 2x)) = x2 81 + 18x + x2 + ((-9 * -9 + 2x * -9) + 2x * (-9 + 2x)) = x2 81 + 18x + x2 + ((81 + -18x) + 2x * (-9 + 2x)) = x2 81 + 18x + x2 + (81 + -18x + (-9 * 2x + 2x * 2x)) = x2 81 + 18x + x2 + (81 + -18x + (-18x + 4x2)) = x2 Combine like terms: -18x + -18x = -36x 81 + 18x + x2 + (81 + -36x + 4x2) = x2 Reorder the terms: 81 + 81 + 18x + -36x + x2 + 4x2 = x2 Combine like terms: 81 + 81 = 162 162 + 18x + -36x + x2 + 4x2 = x2 Combine like terms: 18x + -36x = -18x 162 + -18x + x2 + 4x2 = x2 Combine like terms: x2 + 4x2 = 5x2 162 + -18x + 5x2 = x2 Solving 162 + -18x + 5x2 = x2 Solving for variable 'x'. Combine like terms: 5x2 + -1x2 = 4x2 162 + -18x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 162 + -18x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(81 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying 81 + -9x + 2x2 = 0 Solving 81 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 40.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + -4.5x + -40.5 + x2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + -4.5x + x2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + -4.5x + x2 = 0 + -40.5 -4.5x + x2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 -4.5x + x2 = -40.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -40.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -40.5 + 5.0625 Combine like terms: -40.5 + 5.0625 = -35.4375 5.0625 + -4.5x + x2 = -35.4375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -35.4375 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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