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Simplifying 800 = 0.638x2 + 6.671x + 627.619 Reorder the terms: 800 = 627.619 + 6.671x + 0.638x2 Solving 800 = 627.619 + 6.671x + 0.638x2 Solving for variable 'x'. Combine like terms: 800 + -627.619 = 172.381 172.381 + -6.671x + -0.638x2 = 627.619 + 6.671x + 0.638x2 + -627.619 + -6.671x + -0.638x2 Reorder the terms: 172.381 + -6.671x + -0.638x2 = 627.619 + -627.619 + 6.671x + -6.671x + 0.638x2 + -0.638x2 Combine like terms: 627.619 + -627.619 = 0.000 172.381 + -6.671x + -0.638x2 = 0.000 + 6.671x + -6.671x + 0.638x2 + -0.638x2 172.381 + -6.671x + -0.638x2 = 6.671x + -6.671x + 0.638x2 + -0.638x2 Combine like terms: 6.671x + -6.671x = 0.000 172.381 + -6.671x + -0.638x2 = 0.000 + 0.638x2 + -0.638x2 172.381 + -6.671x + -0.638x2 = 0.638x2 + -0.638x2 Combine like terms: 0.638x2 + -0.638x2 = 0.000 172.381 + -6.671x + -0.638x2 = 0.000 Begin completing the square. Divide all terms by -0.638 the coefficient of the squared term: Divide each side by '-0.638'. -270.1896552 + 10.45611285x + x2 = 0 Move the constant term to the right: Add '270.1896552' to each side of the equation. -270.1896552 + 10.45611285x + 270.1896552 + x2 = 0 + 270.1896552 Reorder the terms: -270.1896552 + 270.1896552 + 10.45611285x + x2 = 0 + 270.1896552 Combine like terms: -270.1896552 + 270.1896552 = 0.0000000 0.0000000 + 10.45611285x + x2 = 0 + 270.1896552 10.45611285x + x2 = 0 + 270.1896552 Combine like terms: 0 + 270.1896552 = 270.1896552 10.45611285x + x2 = 270.1896552 The x term is 10.45611285x. Take half its coefficient (5.228056425). Square it (27.33257398) and add it to both sides. Add '27.33257398' to each side of the equation. 10.45611285x + 27.33257398 + x2 = 270.1896552 + 27.33257398 Reorder the terms: 27.33257398 + 10.45611285x + x2 = 270.1896552 + 27.33257398 Combine like terms: 270.1896552 + 27.33257398 = 297.52222918 27.33257398 + 10.45611285x + x2 = 297.52222918 Factor a perfect square on the left side: (x + 5.228056425)(x + 5.228056425) = 297.52222918 Calculate the square root of the right side: 17.24883269 Break this problem into two subproblems by setting (x + 5.228056425) equal to 17.24883269 and -17.24883269.Subproblem 1
x + 5.228056425 = 17.24883269 Simplifying x + 5.228056425 = 17.24883269 Reorder the terms: 5.228056425 + x = 17.24883269 Solving 5.228056425 + x = 17.24883269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.228056425' to each side of the equation. 5.228056425 + -5.228056425 + x = 17.24883269 + -5.228056425 Combine like terms: 5.228056425 + -5.228056425 = 0.000000000 0.000000000 + x = 17.24883269 + -5.228056425 x = 17.24883269 + -5.228056425 Combine like terms: 17.24883269 + -5.228056425 = 12.020776265 x = 12.020776265 Simplifying x = 12.020776265Subproblem 2
x + 5.228056425 = -17.24883269 Simplifying x + 5.228056425 = -17.24883269 Reorder the terms: 5.228056425 + x = -17.24883269 Solving 5.228056425 + x = -17.24883269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.228056425' to each side of the equation. 5.228056425 + -5.228056425 + x = -17.24883269 + -5.228056425 Combine like terms: 5.228056425 + -5.228056425 = 0.000000000 0.000000000 + x = -17.24883269 + -5.228056425 x = -17.24883269 + -5.228056425 Combine like terms: -17.24883269 + -5.228056425 = -22.476889115 x = -22.476889115 Simplifying x = -22.476889115Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.020776265, -22.476889115}
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