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Simplifying ((4x + 9)(4x + 9)) + 25 = 0 Reorder the terms: ((9 + 4x)(4x + 9)) + 25 = 0 Reorder the terms: ((9 + 4x)(9 + 4x)) + 25 = 0 Multiply (9 + 4x) * (9 + 4x) ((9(9 + 4x) + 4x * (9 + 4x))) + 25 = 0 (((9 * 9 + 4x * 9) + 4x * (9 + 4x))) + 25 = 0 (((81 + 36x) + 4x * (9 + 4x))) + 25 = 0 ((81 + 36x + (9 * 4x + 4x * 4x))) + 25 = 0 ((81 + 36x + (36x + 16x2))) + 25 = 0 Combine like terms: 36x + 36x = 72x ((81 + 72x + 16x2)) + 25 = 0 (81 + 72x + 16x2) + 25 = 0 Remove parenthesis around (81 + 72x + 16x2) 81 + 72x + 16x2 + 25 = 0 Reorder the terms: 81 + 25 + 72x + 16x2 = 0 Combine like terms: 81 + 25 = 106 106 + 72x + 16x2 = 0 Solving 106 + 72x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(53 + 36x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(53 + 36x + 8x2)' equal to zero and attempt to solve: Simplifying 53 + 36x + 8x2 = 0 Solving 53 + 36x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.625 + 4.5x + x2 = 0 Move the constant term to the right: Add '-6.625' to each side of the equation. 6.625 + 4.5x + -6.625 + x2 = 0 + -6.625 Reorder the terms: 6.625 + -6.625 + 4.5x + x2 = 0 + -6.625 Combine like terms: 6.625 + -6.625 = 0.000 0.000 + 4.5x + x2 = 0 + -6.625 4.5x + x2 = 0 + -6.625 Combine like terms: 0 + -6.625 = -6.625 4.5x + x2 = -6.625 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 = -6.625 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -6.625 + 5.0625 Combine like terms: -6.625 + 5.0625 = -1.5625 5.0625 + 4.5x + x2 = -1.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -1.5625 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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