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Simplifying 36x2 + -748x + -2465 = 0 Reorder the terms: -2465 + -748x + 36x2 = 0 Solving -2465 + -748x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -68.47222222 + -20.77777778x + x2 = 0 Move the constant term to the right: Add '68.47222222' to each side of the equation. -68.47222222 + -20.77777778x + 68.47222222 + x2 = 0 + 68.47222222 Reorder the terms: -68.47222222 + 68.47222222 + -20.77777778x + x2 = 0 + 68.47222222 Combine like terms: -68.47222222 + 68.47222222 = 0.00000000 0.00000000 + -20.77777778x + x2 = 0 + 68.47222222 -20.77777778x + x2 = 0 + 68.47222222 Combine like terms: 0 + 68.47222222 = 68.47222222 -20.77777778x + x2 = 68.47222222 The x term is -20.77777778x. Take half its coefficient (-10.38888889). Square it (107.9290124) and add it to both sides. Add '107.9290124' to each side of the equation. -20.77777778x + 107.9290124 + x2 = 68.47222222 + 107.9290124 Reorder the terms: 107.9290124 + -20.77777778x + x2 = 68.47222222 + 107.9290124 Combine like terms: 68.47222222 + 107.9290124 = 176.40123462 107.9290124 + -20.77777778x + x2 = 176.40123462 Factor a perfect square on the left side: (x + -10.38888889)(x + -10.38888889) = 176.40123462 Calculate the square root of the right side: 13.281612651 Break this problem into two subproblems by setting (x + -10.38888889) equal to 13.281612651 and -13.281612651.Subproblem 1
x + -10.38888889 = 13.281612651 Simplifying x + -10.38888889 = 13.281612651 Reorder the terms: -10.38888889 + x = 13.281612651 Solving -10.38888889 + x = 13.281612651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.38888889' to each side of the equation. -10.38888889 + 10.38888889 + x = 13.281612651 + 10.38888889 Combine like terms: -10.38888889 + 10.38888889 = 0.00000000 0.00000000 + x = 13.281612651 + 10.38888889 x = 13.281612651 + 10.38888889 Combine like terms: 13.281612651 + 10.38888889 = 23.670501541 x = 23.670501541 Simplifying x = 23.670501541Subproblem 2
x + -10.38888889 = -13.281612651 Simplifying x + -10.38888889 = -13.281612651 Reorder the terms: -10.38888889 + x = -13.281612651 Solving -10.38888889 + x = -13.281612651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.38888889' to each side of the equation. -10.38888889 + 10.38888889 + x = -13.281612651 + 10.38888889 Combine like terms: -10.38888889 + 10.38888889 = 0.00000000 0.00000000 + x = -13.281612651 + 10.38888889 x = -13.281612651 + 10.38888889 Combine like terms: -13.281612651 + 10.38888889 = -2.892723761 x = -2.892723761 Simplifying x = -2.892723761Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.670501541, -2.892723761}
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