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Simplifying (4x + 9)(4x + 9) + 49 = 0 Reorder the terms: (9 + 4x)(4x + 9) + 49 = 0 Reorder the terms: (9 + 4x)(9 + 4x) + 49 = 0 Multiply (9 + 4x) * (9 + 4x) (9(9 + 4x) + 4x * (9 + 4x)) + 49 = 0 ((9 * 9 + 4x * 9) + 4x * (9 + 4x)) + 49 = 0 ((81 + 36x) + 4x * (9 + 4x)) + 49 = 0 (81 + 36x + (9 * 4x + 4x * 4x)) + 49 = 0 (81 + 36x + (36x + 16x2)) + 49 = 0 Combine like terms: 36x + 36x = 72x (81 + 72x + 16x2) + 49 = 0 Reorder the terms: 81 + 49 + 72x + 16x2 = 0 Combine like terms: 81 + 49 = 130 130 + 72x + 16x2 = 0 Solving 130 + 72x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(65 + 36x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(65 + 36x + 8x2)' equal to zero and attempt to solve: Simplifying 65 + 36x + 8x2 = 0 Solving 65 + 36x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 8.125 + 4.5x + x2 = 0 Move the constant term to the right: Add '-8.125' to each side of the equation. 8.125 + 4.5x + -8.125 + x2 = 0 + -8.125 Reorder the terms: 8.125 + -8.125 + 4.5x + x2 = 0 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + 4.5x + x2 = 0 + -8.125 4.5x + x2 = 0 + -8.125 Combine like terms: 0 + -8.125 = -8.125 4.5x + x2 = -8.125 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 = -8.125 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -8.125 + 5.0625 Combine like terms: -8.125 + 5.0625 = -3.0625 5.0625 + 4.5x + x2 = -3.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -3.0625 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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