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Simplifying 784 = -16x2 + 56x Reorder the terms: 784 = 56x + -16x2 Solving 784 = 56x + -16x2 Solving for variable 'x'. Reorder the terms: 784 + -56x + 16x2 = 56x + -56x + -16x2 + 16x2 Combine like terms: 56x + -56x = 0 784 + -56x + 16x2 = 0 + -16x2 + 16x2 784 + -56x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 784 + -56x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(98 + -7x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(98 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 98 + -7x + 2x2 = 0 Solving 98 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 49 + -3.5x + x2 = 0 Move the constant term to the right: Add '-49' to each side of the equation. 49 + -3.5x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -3.5x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -3.5x + x2 = 0 + -49 -3.5x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -3.5x + x2 = -49 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 = -49 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -49 + 3.0625 Combine like terms: -49 + 3.0625 = -45.9375 3.0625 + -3.5x + x2 = -45.9375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -45.9375 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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