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Simplifying -9x2 + 39.85x + -40 = 0 Reorder the terms: -40 + 39.85x + -9x2 = 0 Solving -40 + 39.85x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 4.444444444 + -4.427777778x + x2 = 0 Move the constant term to the right: Add '-4.444444444' to each side of the equation. 4.444444444 + -4.427777778x + -4.444444444 + x2 = 0 + -4.444444444 Reorder the terms: 4.444444444 + -4.444444444 + -4.427777778x + x2 = 0 + -4.444444444 Combine like terms: 4.444444444 + -4.444444444 = 0.000000000 0.000000000 + -4.427777778x + x2 = 0 + -4.444444444 -4.427777778x + x2 = 0 + -4.444444444 Combine like terms: 0 + -4.444444444 = -4.444444444 -4.427777778x + x2 = -4.444444444 The x term is -4.427777778x. Take half its coefficient (-2.213888889). Square it (4.901304013) and add it to both sides. Add '4.901304013' to each side of the equation. -4.427777778x + 4.901304013 + x2 = -4.444444444 + 4.901304013 Reorder the terms: 4.901304013 + -4.427777778x + x2 = -4.444444444 + 4.901304013 Combine like terms: -4.444444444 + 4.901304013 = 0.456859569 4.901304013 + -4.427777778x + x2 = 0.456859569 Factor a perfect square on the left side: (x + -2.213888889)(x + -2.213888889) = 0.456859569 Calculate the square root of the right side: 0.675913877 Break this problem into two subproblems by setting (x + -2.213888889) equal to 0.675913877 and -0.675913877.Subproblem 1
x + -2.213888889 = 0.675913877 Simplifying x + -2.213888889 = 0.675913877 Reorder the terms: -2.213888889 + x = 0.675913877 Solving -2.213888889 + x = 0.675913877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.213888889' to each side of the equation. -2.213888889 + 2.213888889 + x = 0.675913877 + 2.213888889 Combine like terms: -2.213888889 + 2.213888889 = 0.000000000 0.000000000 + x = 0.675913877 + 2.213888889 x = 0.675913877 + 2.213888889 Combine like terms: 0.675913877 + 2.213888889 = 2.889802766 x = 2.889802766 Simplifying x = 2.889802766Subproblem 2
x + -2.213888889 = -0.675913877 Simplifying x + -2.213888889 = -0.675913877 Reorder the terms: -2.213888889 + x = -0.675913877 Solving -2.213888889 + x = -0.675913877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.213888889' to each side of the equation. -2.213888889 + 2.213888889 + x = -0.675913877 + 2.213888889 Combine like terms: -2.213888889 + 2.213888889 = 0.000000000 0.000000000 + x = -0.675913877 + 2.213888889 x = -0.675913877 + 2.213888889 Combine like terms: -0.675913877 + 2.213888889 = 1.537975012 x = 1.537975012 Simplifying x = 1.537975012Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.889802766, 1.537975012}
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