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Simplifying 80 = -23.944 + 0.199x + -0.00008x2 Solving 80 = -23.944 + 0.199x + -0.00008x2 Solving for variable 'x'. Combine like terms: 80 + 23.944 = 103.944 103.944 + -0.199x + 0.00008x2 = -23.944 + 0.199x + -0.00008x2 + 23.944 + -0.199x + 0.00008x2 Reorder the terms: 103.944 + -0.199x + 0.00008x2 = -23.944 + 23.944 + 0.199x + -0.199x + -0.00008x2 + 0.00008x2 Combine like terms: -23.944 + 23.944 = 0.000 103.944 + -0.199x + 0.00008x2 = 0.000 + 0.199x + -0.199x + -0.00008x2 + 0.00008x2 103.944 + -0.199x + 0.00008x2 = 0.199x + -0.199x + -0.00008x2 + 0.00008x2 Combine like terms: 0.199x + -0.199x = 0.000 103.944 + -0.199x + 0.00008x2 = 0.000 + -0.00008x2 + 0.00008x2 103.944 + -0.199x + 0.00008x2 = -0.00008x2 + 0.00008x2 Combine like terms: -0.00008x2 + 0.00008x2 = 0.00000 103.944 + -0.199x + 0.00008x2 = 0.00000 Begin completing the square. Divide all terms by 0.00008 the coefficient of the squared term: Divide each side by '0.00008'. 1299300 + -2487.5x + x2 = 0 Move the constant term to the right: Add '-1299300' to each side of the equation. 1299300 + -2487.5x + -1299300 + x2 = 0 + -1299300 Reorder the terms: 1299300 + -1299300 + -2487.5x + x2 = 0 + -1299300 Combine like terms: 1299300 + -1299300 = 0 0 + -2487.5x + x2 = 0 + -1299300 -2487.5x + x2 = 0 + -1299300 Combine like terms: 0 + -1299300 = -1299300 -2487.5x + x2 = -1299300 The x term is -2487.5x. Take half its coefficient (-1243.75). Square it (1546914.063) and add it to both sides. Add '1546914.063' to each side of the equation. -2487.5x + 1546914.063 + x2 = -1299300 + 1546914.063 Reorder the terms: 1546914.063 + -2487.5x + x2 = -1299300 + 1546914.063 Combine like terms: -1299300 + 1546914.063 = 247614.063 1546914.063 + -2487.5x + x2 = 247614.063 Factor a perfect square on the left side: (x + -1243.75)(x + -1243.75) = 247614.063 Calculate the square root of the right side: 497.608342977 Break this problem into two subproblems by setting (x + -1243.75) equal to 497.608342977 and -497.608342977.Subproblem 1
x + -1243.75 = 497.608342977 Simplifying x + -1243.75 = 497.608342977 Reorder the terms: -1243.75 + x = 497.608342977 Solving -1243.75 + x = 497.608342977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1243.75' to each side of the equation. -1243.75 + 1243.75 + x = 497.608342977 + 1243.75 Combine like terms: -1243.75 + 1243.75 = 0.00 0.00 + x = 497.608342977 + 1243.75 x = 497.608342977 + 1243.75 Combine like terms: 497.608342977 + 1243.75 = 1741.358342977 x = 1741.358342977 Simplifying x = 1741.358342977Subproblem 2
x + -1243.75 = -497.608342977 Simplifying x + -1243.75 = -497.608342977 Reorder the terms: -1243.75 + x = -497.608342977 Solving -1243.75 + x = -497.608342977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1243.75' to each side of the equation. -1243.75 + 1243.75 + x = -497.608342977 + 1243.75 Combine like terms: -1243.75 + 1243.75 = 0.00 0.00 + x = -497.608342977 + 1243.75 x = -497.608342977 + 1243.75 Combine like terms: -497.608342977 + 1243.75 = 746.141657023 x = 746.141657023 Simplifying x = 746.141657023Solution
The solution to the problem is based on the solutions from the subproblems. x = {1741.358342977, 746.141657023}
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