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Simplifying 16x2 + 88x + 224 = 0 Reorder the terms: 224 + 88x + 16x2 = 0 Solving 224 + 88x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(28 + 11x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(28 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying 28 + 11x + 2x2 = 0 Solving 28 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14 + 5.5x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 5.5x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 5.5x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 5.5x + x2 = 0 + -14 5.5x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 5.5x + x2 = -14 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -14 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -14 + 7.5625 Combine like terms: -14 + 7.5625 = -6.4375 7.5625 + 5.5x + x2 = -6.4375 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = -6.4375 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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