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Simplifying 0 = x2 + 16x + 65 Reorder the terms: 0 = 65 + 16x + x2 Solving 0 = 65 + 16x + x2 Solving for variable 'x'. Combine like terms: 0 + -65 = -65 -65 + -16x + -1x2 = 65 + 16x + x2 + -65 + -16x + -1x2 Reorder the terms: -65 + -16x + -1x2 = 65 + -65 + 16x + -16x + x2 + -1x2 Combine like terms: 65 + -65 = 0 -65 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 -65 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 -65 + -16x + -1x2 = 0 + x2 + -1x2 -65 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -65 + -16x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(65 + 16x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(65 + 16x + x2)' equal to zero and attempt to solve: Simplifying 65 + 16x + x2 = 0 Solving 65 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-65' to each side of the equation. 65 + 16x + -65 + x2 = 0 + -65 Reorder the terms: 65 + -65 + 16x + x2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + 16x + x2 = 0 + -65 16x + x2 = 0 + -65 Combine like terms: 0 + -65 = -65 16x + x2 = -65 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 = -65 + 64 Reorder the terms: 64 + 16x + x2 = -65 + 64 Combine like terms: -65 + 64 = -1 64 + 16x + x2 = -1 Factor a perfect square on the left side: (x + 8)(x + 8) = -1 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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