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Simplifying 0 = (x + 9)(x + 9) + 2 Reorder the terms: 0 = (9 + x)(x + 9) + 2 Reorder the terms: 0 = (9 + x)(9 + x) + 2 Multiply (9 + x) * (9 + x) 0 = (9(9 + x) + x(9 + x)) + 2 0 = ((9 * 9 + x * 9) + x(9 + x)) + 2 0 = ((81 + 9x) + x(9 + x)) + 2 0 = (81 + 9x + (9 * x + x * x)) + 2 0 = (81 + 9x + (9x + x2)) + 2 Combine like terms: 9x + 9x = 18x 0 = (81 + 18x + x2) + 2 Reorder the terms: 0 = 81 + 2 + 18x + x2 Combine like terms: 81 + 2 = 83 0 = 83 + 18x + x2 Solving 0 = 83 + 18x + x2 Solving for variable 'x'. Combine like terms: 0 + -83 = -83 -83 + -18x + -1x2 = 83 + 18x + x2 + -83 + -18x + -1x2 Reorder the terms: -83 + -18x + -1x2 = 83 + -83 + 18x + -18x + x2 + -1x2 Combine like terms: 83 + -83 = 0 -83 + -18x + -1x2 = 0 + 18x + -18x + x2 + -1x2 -83 + -18x + -1x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 -83 + -18x + -1x2 = 0 + x2 + -1x2 -83 + -18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -83 + -18x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(83 + 18x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(83 + 18x + x2)' equal to zero and attempt to solve: Simplifying 83 + 18x + x2 = 0 Solving 83 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-83' to each side of the equation. 83 + 18x + -83 + x2 = 0 + -83 Reorder the terms: 83 + -83 + 18x + x2 = 0 + -83 Combine like terms: 83 + -83 = 0 0 + 18x + x2 = 0 + -83 18x + x2 = 0 + -83 Combine like terms: 0 + -83 = -83 18x + x2 = -83 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -83 + 81 Reorder the terms: 81 + 18x + x2 = -83 + 81 Combine like terms: -83 + 81 = -2 81 + 18x + x2 = -2 Factor a perfect square on the left side: (x + 9)(x + 9) = -2 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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