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Simplifying (-1.665x2) + 33.626x + -102.861 = 0 Reorder the terms: -102.861 + 33.626x + (-1.665x2) = 0 Solving -102.861 + 33.626x + (-1.665x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.665 the coefficient of the squared term: Divide each side by '-1.665'. 61.77837838 + -20.1957958x + x2 = 0 Move the constant term to the right: Add '-61.77837838' to each side of the equation. 61.77837838 + -20.1957958x + -61.77837838 + x2 = 0 + -61.77837838 Reorder the terms: 61.77837838 + -61.77837838 + -20.1957958x + x2 = 0 + -61.77837838 Combine like terms: 61.77837838 + -61.77837838 = 0.00000000 0.00000000 + -20.1957958x + x2 = 0 + -61.77837838 -20.1957958x + x2 = 0 + -61.77837838 Combine like terms: 0 + -61.77837838 = -61.77837838 -20.1957958x + x2 = -61.77837838 The x term is -20.1957958x. Take half its coefficient (-10.0978979). Square it (101.9675420) and add it to both sides. Add '101.9675420' to each side of the equation. -20.1957958x + 101.9675420 + x2 = -61.77837838 + 101.9675420 Reorder the terms: 101.9675420 + -20.1957958x + x2 = -61.77837838 + 101.9675420 Combine like terms: -61.77837838 + 101.9675420 = 40.18916362 101.9675420 + -20.1957958x + x2 = 40.18916362 Factor a perfect square on the left side: ((x) + -10.0978979)((x) + -10.0978979) = 40.18916362 Calculate the square root of the right side: 6.339492379 Break this problem into two subproblems by setting ((x) + -10.0978979) equal to 6.339492379 and -6.339492379.Subproblem 1
(x) + -10.0978979 = 6.339492379 Simplifying (x) + -10.0978979 = 6.339492379 x + -10.0978979 = 6.339492379 Reorder the terms: -10.0978979 + x = 6.339492379 Solving -10.0978979 + x = 6.339492379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.0978979' to each side of the equation. -10.0978979 + 10.0978979 + x = 6.339492379 + 10.0978979 Combine like terms: -10.0978979 + 10.0978979 = 0.0000000 0.0000000 + x = 6.339492379 + 10.0978979 x = 6.339492379 + 10.0978979 Combine like terms: 6.339492379 + 10.0978979 = 16.437390279 x = 16.437390279 Simplifying x = 16.437390279Subproblem 2
(x) + -10.0978979 = -6.339492379 Simplifying (x) + -10.0978979 = -6.339492379 x + -10.0978979 = -6.339492379 Reorder the terms: -10.0978979 + x = -6.339492379 Solving -10.0978979 + x = -6.339492379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.0978979' to each side of the equation. -10.0978979 + 10.0978979 + x = -6.339492379 + 10.0978979 Combine like terms: -10.0978979 + 10.0978979 = 0.0000000 0.0000000 + x = -6.339492379 + 10.0978979 x = -6.339492379 + 10.0978979 Combine like terms: -6.339492379 + 10.0978979 = 3.758405521 x = 3.758405521 Simplifying x = 3.758405521Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.437390279, 3.758405521}
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