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Simplifying 20 = -2x2 + 16x + -31 Reorder the terms: 20 = -31 + 16x + -2x2 Solving 20 = -31 + 16x + -2x2 Solving for variable 'x'. Combine like terms: 20 + 31 = 51 51 + -16x + 2x2 = -31 + 16x + -2x2 + 31 + -16x + 2x2 Reorder the terms: 51 + -16x + 2x2 = -31 + 31 + 16x + -16x + -2x2 + 2x2 Combine like terms: -31 + 31 = 0 51 + -16x + 2x2 = 0 + 16x + -16x + -2x2 + 2x2 51 + -16x + 2x2 = 16x + -16x + -2x2 + 2x2 Combine like terms: 16x + -16x = 0 51 + -16x + 2x2 = 0 + -2x2 + 2x2 51 + -16x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 51 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25.5 + -8x + x2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + -8x + -25.5 + x2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + -8x + x2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + -8x + x2 = 0 + -25.5 -8x + x2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 -8x + x2 = -25.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -25.5 + 16 Reorder the terms: 16 + -8x + x2 = -25.5 + 16 Combine like terms: -25.5 + 16 = -9.5 16 + -8x + x2 = -9.5 Factor a perfect square on the left side: (x + -4)(x + -4) = -9.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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