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Simplifying (x + 16)(x + 16) + x2 = 12 Reorder the terms: (16 + x)(x + 16) + x2 = 12 Reorder the terms: (16 + x)(16 + x) + x2 = 12 Multiply (16 + x) * (16 + x) (16(16 + x) + x(16 + x)) + x2 = 12 ((16 * 16 + x * 16) + x(16 + x)) + x2 = 12 ((256 + 16x) + x(16 + x)) + x2 = 12 (256 + 16x + (16 * x + x * x)) + x2 = 12 (256 + 16x + (16x + x2)) + x2 = 12 Combine like terms: 16x + 16x = 32x (256 + 32x + x2) + x2 = 12 Combine like terms: x2 + x2 = 2x2 256 + 32x + 2x2 = 12 Solving 256 + 32x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: 256 + -12 + 32x + 2x2 = 12 + -12 Combine like terms: 256 + -12 = 244 244 + 32x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 244 + 32x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(122 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(122 + 16x + x2)' equal to zero and attempt to solve: Simplifying 122 + 16x + x2 = 0 Solving 122 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-122' to each side of the equation. 122 + 16x + -122 + x2 = 0 + -122 Reorder the terms: 122 + -122 + 16x + x2 = 0 + -122 Combine like terms: 122 + -122 = 0 0 + 16x + x2 = 0 + -122 16x + x2 = 0 + -122 Combine like terms: 0 + -122 = -122 16x + x2 = -122 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -122 + 64 Reorder the terms: 64 + 16x + x2 = -122 + 64 Combine like terms: -122 + 64 = -58 64 + 16x + x2 = -58 Factor a perfect square on the left side: (x + 8)(x + 8) = -58 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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