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Simplifying (2x + 9)(2x + 9) + 9 = 0 Reorder the terms: (9 + 2x)(2x + 9) + 9 = 0 Reorder the terms: (9 + 2x)(9 + 2x) + 9 = 0 Multiply (9 + 2x) * (9 + 2x) (9(9 + 2x) + 2x * (9 + 2x)) + 9 = 0 ((9 * 9 + 2x * 9) + 2x * (9 + 2x)) + 9 = 0 ((81 + 18x) + 2x * (9 + 2x)) + 9 = 0 (81 + 18x + (9 * 2x + 2x * 2x)) + 9 = 0 (81 + 18x + (18x + 4x2)) + 9 = 0 Combine like terms: 18x + 18x = 36x (81 + 36x + 4x2) + 9 = 0 Reorder the terms: 81 + 9 + 36x + 4x2 = 0 Combine like terms: 81 + 9 = 90 90 + 36x + 4x2 = 0 Solving 90 + 36x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + 18x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + 18x + 2x2)' equal to zero and attempt to solve: Simplifying 45 + 18x + 2x2 = 0 Solving 45 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 9x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 9x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 9x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 9x + x2 = 0 + -22.5 9x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 9x + x2 = -22.5 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -22.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -22.5 + 20.25 Combine like terms: -22.5 + 20.25 = -2.25 20.25 + 9x + x2 = -2.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = -2.25 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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