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Simplifying 8(x2 + 14x + 117) = 0 Reorder the terms: 8(117 + 14x + x2) = 0 (117 * 8 + 14x * 8 + x2 * 8) = 0 (936 + 112x + 8x2) = 0 Solving 936 + 112x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(117 + 14x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(117 + 14x + x2)' equal to zero and attempt to solve: Simplifying 117 + 14x + x2 = 0 Solving 117 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-117' to each side of the equation. 117 + 14x + -117 + x2 = 0 + -117 Reorder the terms: 117 + -117 + 14x + x2 = 0 + -117 Combine like terms: 117 + -117 = 0 0 + 14x + x2 = 0 + -117 14x + x2 = 0 + -117 Combine like terms: 0 + -117 = -117 14x + x2 = -117 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -117 + 49 Reorder the terms: 49 + 14x + x2 = -117 + 49 Combine like terms: -117 + 49 = -68 49 + 14x + x2 = -68 Factor a perfect square on the left side: (x + 7)(x + 7) = -68 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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