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Simplifying 1990 = -2.02x2 + 77.85x + 746 Reorder the terms: 1990 = 746 + 77.85x + -2.02x2 Solving 1990 = 746 + 77.85x + -2.02x2 Solving for variable 'x'. Combine like terms: 1990 + -746 = 1244 1244 + -77.85x + 2.02x2 = 746 + 77.85x + -2.02x2 + -746 + -77.85x + 2.02x2 Reorder the terms: 1244 + -77.85x + 2.02x2 = 746 + -746 + 77.85x + -77.85x + -2.02x2 + 2.02x2 Combine like terms: 746 + -746 = 0 1244 + -77.85x + 2.02x2 = 0 + 77.85x + -77.85x + -2.02x2 + 2.02x2 1244 + -77.85x + 2.02x2 = 77.85x + -77.85x + -2.02x2 + 2.02x2 Combine like terms: 77.85x + -77.85x = 0.00 1244 + -77.85x + 2.02x2 = 0.00 + -2.02x2 + 2.02x2 1244 + -77.85x + 2.02x2 = -2.02x2 + 2.02x2 Combine like terms: -2.02x2 + 2.02x2 = 0.00 1244 + -77.85x + 2.02x2 = 0.00 Begin completing the square. Divide all terms by 2.02 the coefficient of the squared term: Divide each side by '2.02'. 615.8415842 + -38.53960396x + x2 = 0 Move the constant term to the right: Add '-615.8415842' to each side of the equation. 615.8415842 + -38.53960396x + -615.8415842 + x2 = 0 + -615.8415842 Reorder the terms: 615.8415842 + -615.8415842 + -38.53960396x + x2 = 0 + -615.8415842 Combine like terms: 615.8415842 + -615.8415842 = 0.0000000 0.0000000 + -38.53960396x + x2 = 0 + -615.8415842 -38.53960396x + x2 = 0 + -615.8415842 Combine like terms: 0 + -615.8415842 = -615.8415842 -38.53960396x + x2 = -615.8415842 The x term is -38.53960396x. Take half its coefficient (-19.26980198). Square it (371.3252683) and add it to both sides. Add '371.3252683' to each side of the equation. -38.53960396x + 371.3252683 + x2 = -615.8415842 + 371.3252683 Reorder the terms: 371.3252683 + -38.53960396x + x2 = -615.8415842 + 371.3252683 Combine like terms: -615.8415842 + 371.3252683 = -244.5163159 371.3252683 + -38.53960396x + x2 = -244.5163159 Factor a perfect square on the left side: (x + -19.26980198)(x + -19.26980198) = -244.5163159 Can't calculate square root of the right side. The solution to this equation could not be determined.
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