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Simplifying 35x2 + 9 = 65x + 91 Reorder the terms: 9 + 35x2 = 65x + 91 Reorder the terms: 9 + 35x2 = 91 + 65x Solving 9 + 35x2 = 91 + 65x Solving for variable 'x'. Reorder the terms: 9 + -91 + -65x + 35x2 = 91 + 65x + -91 + -65x Combine like terms: 9 + -91 = -82 -82 + -65x + 35x2 = 91 + 65x + -91 + -65x Reorder the terms: -82 + -65x + 35x2 = 91 + -91 + 65x + -65x Combine like terms: 91 + -91 = 0 -82 + -65x + 35x2 = 0 + 65x + -65x -82 + -65x + 35x2 = 65x + -65x Combine like terms: 65x + -65x = 0 -82 + -65x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -2.342857143 + -1.857142857x + x2 = 0 Move the constant term to the right: Add '2.342857143' to each side of the equation. -2.342857143 + -1.857142857x + 2.342857143 + x2 = 0 + 2.342857143 Reorder the terms: -2.342857143 + 2.342857143 + -1.857142857x + x2 = 0 + 2.342857143 Combine like terms: -2.342857143 + 2.342857143 = 0.000000000 0.000000000 + -1.857142857x + x2 = 0 + 2.342857143 -1.857142857x + x2 = 0 + 2.342857143 Combine like terms: 0 + 2.342857143 = 2.342857143 -1.857142857x + x2 = 2.342857143 The x term is -1.857142857x. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857x + 0.8622448978 + x2 = 2.342857143 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x + x2 = 2.342857143 + 0.8622448978 Combine like terms: 2.342857143 + 0.8622448978 = 3.2051020408 0.8622448978 + -1.857142857x + x2 = 3.2051020408 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 3.2051020408 Calculate the square root of the right side: 1.790279878 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 1.790279878 and -1.790279878.Subproblem 1
x + -0.9285714285 = 1.790279878 Simplifying x + -0.9285714285 = 1.790279878 Reorder the terms: -0.9285714285 + x = 1.790279878 Solving -0.9285714285 + x = 1.790279878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = 1.790279878 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 1.790279878 + 0.9285714285 x = 1.790279878 + 0.9285714285 Combine like terms: 1.790279878 + 0.9285714285 = 2.7188513065 x = 2.7188513065 Simplifying x = 2.7188513065Subproblem 2
x + -0.9285714285 = -1.790279878 Simplifying x + -0.9285714285 = -1.790279878 Reorder the terms: -0.9285714285 + x = -1.790279878 Solving -0.9285714285 + x = -1.790279878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = -1.790279878 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -1.790279878 + 0.9285714285 x = -1.790279878 + 0.9285714285 Combine like terms: -1.790279878 + 0.9285714285 = -0.8617084495 x = -0.8617084495 Simplifying x = -0.8617084495Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7188513065, -0.8617084495}
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