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Simplifying 15 = -16x2 + 20x + 5.5 Reorder the terms: 15 = 5.5 + 20x + -16x2 Solving 15 = 5.5 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 15 + -5.5 = 9.5 9.5 + -20x + 16x2 = 5.5 + 20x + -16x2 + -5.5 + -20x + 16x2 Reorder the terms: 9.5 + -20x + 16x2 = 5.5 + -5.5 + 20x + -20x + -16x2 + 16x2 Combine like terms: 5.5 + -5.5 = 0.0 9.5 + -20x + 16x2 = 0.0 + 20x + -20x + -16x2 + 16x2 9.5 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 9.5 + -20x + 16x2 = 0 + -16x2 + 16x2 9.5 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 9.5 + -20x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.59375 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.59375' to each side of the equation. 0.59375 + -1.25x + -0.59375 + x2 = 0 + -0.59375 Reorder the terms: 0.59375 + -0.59375 + -1.25x + x2 = 0 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + -1.25x + x2 = 0 + -0.59375 -1.25x + x2 = 0 + -0.59375 Combine like terms: 0 + -0.59375 = -0.59375 -1.25x + x2 = -0.59375 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.59375 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.59375 + 0.390625 Combine like terms: -0.59375 + 0.390625 = -0.203125 0.390625 + -1.25x + x2 = -0.203125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -0.203125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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