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Simplifying 16x2 + 10x + 56 = 0 Reorder the terms: 56 + 10x + 16x2 = 0 Solving 56 + 10x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(28 + 5x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + 5x + 8x2)' equal to zero and attempt to solve: Simplifying 28 + 5x + 8x2 = 0 Solving 28 + 5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.5 + 0.625x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 0.625x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 0.625x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 0.625x + x2 = 0 + -3.5 0.625x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 0.625x + x2 = -3.5 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = -3.5 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = -3.5 + 0.09765625 Combine like terms: -3.5 + 0.09765625 = -3.40234375 0.09765625 + 0.625x + x2 = -3.40234375 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = -3.40234375 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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