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Simplifying 16x2 + 50x + 100 = 0 Reorder the terms: 100 + 50x + 16x2 = 0 Solving 100 + 50x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 25x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 25x + 8x2)' equal to zero and attempt to solve: Simplifying 50 + 25x + 8x2 = 0 Solving 50 + 25x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.25 + 3.125x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 3.125x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 3.125x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 3.125x + x2 = 0 + -6.25 3.125x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 3.125x + x2 = -6.25 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = -6.25 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = -6.25 + 2.44140625 Combine like terms: -6.25 + 2.44140625 = -3.80859375 2.44140625 + 3.125x + x2 = -3.80859375 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = -3.80859375 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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