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Simplifying 276 = -16x2 + 72x Reorder the terms: 276 = 72x + -16x2 Solving 276 = 72x + -16x2 Solving for variable 'x'. Reorder the terms: 276 + -72x + 16x2 = 72x + -72x + -16x2 + 16x2 Combine like terms: 72x + -72x = 0 276 + -72x + 16x2 = 0 + -16x2 + 16x2 276 + -72x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 276 + -72x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(69 + -18x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(69 + -18x + 4x2)' equal to zero and attempt to solve: Simplifying 69 + -18x + 4x2 = 0 Solving 69 + -18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 17.25 + -4.5x + x2 = 0 Move the constant term to the right: Add '-17.25' to each side of the equation. 17.25 + -4.5x + -17.25 + x2 = 0 + -17.25 Reorder the terms: 17.25 + -17.25 + -4.5x + x2 = 0 + -17.25 Combine like terms: 17.25 + -17.25 = 0.00 0.00 + -4.5x + x2 = 0 + -17.25 -4.5x + x2 = 0 + -17.25 Combine like terms: 0 + -17.25 = -17.25 -4.5x + x2 = -17.25 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -17.25 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -17.25 + 5.0625 Combine like terms: -17.25 + 5.0625 = -12.1875 5.0625 + -4.5x + x2 = -12.1875 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -12.1875 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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