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Simplifying 196 = -16x2 + 56x Reorder the terms: 196 = 56x + -16x2 Solving 196 = 56x + -16x2 Solving for variable 'x'. Reorder the terms: 196 + -56x + 16x2 = 56x + -56x + -16x2 + 16x2 Combine like terms: 56x + -56x = 0 196 + -56x + 16x2 = 0 + -16x2 + 16x2 196 + -56x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 196 + -56x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(49 + -14x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(49 + -14x + 4x2)' equal to zero and attempt to solve: Simplifying 49 + -14x + 4x2 = 0 Solving 49 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.25 + -3.5x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -3.5x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -3.5x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -3.5x + x2 = 0 + -12.25 -3.5x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -3.5x + x2 = -12.25 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -12.25 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -12.25 + 3.0625 Combine like terms: -12.25 + 3.0625 = -9.1875 3.0625 + -3.5x + x2 = -9.1875 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -9.1875 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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