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Simplifying 9x2 + -35x + 25 = 0 Reorder the terms: 25 + -35x + 9x2 = 0 Solving 25 + -35x + 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'. 2.777777778 + -3.888888889x + x2 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + -3.888888889x + -2.777777778 + x2 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + -3.888888889x + x2 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + -3.888888889x + x2 = 0 + -2.777777778 -3.888888889x + x2 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 -3.888888889x + x2 = -2.777777778 The x term is -3.888888889x. Take half its coefficient (-1.944444445). Square it (3.780864200) and add it to both sides. Add '3.780864200' to each side of the equation. -3.888888889x + 3.780864200 + x2 = -2.777777778 + 3.780864200 Reorder the terms: 3.780864200 + -3.888888889x + x2 = -2.777777778 + 3.780864200 Combine like terms: -2.777777778 + 3.780864200 = 1.003086422 3.780864200 + -3.888888889x + x2 = 1.003086422 Factor a perfect square on the left side: (x + -1.944444445)(x + -1.944444445) = 1.003086422 Calculate the square root of the right side: 1.001542022 Break this problem into two subproblems by setting (x + -1.944444445) equal to 1.001542022 and -1.001542022.Subproblem 1
x + -1.944444445 = 1.001542022 Simplifying x + -1.944444445 = 1.001542022 Reorder the terms: -1.944444445 + x = 1.001542022 Solving -1.944444445 + x = 1.001542022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = 1.001542022 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = 1.001542022 + 1.944444445 x = 1.001542022 + 1.944444445 Combine like terms: 1.001542022 + 1.944444445 = 2.945986467 x = 2.945986467 Simplifying x = 2.945986467Subproblem 2
x + -1.944444445 = -1.001542022 Simplifying x + -1.944444445 = -1.001542022 Reorder the terms: -1.944444445 + x = -1.001542022 Solving -1.944444445 + x = -1.001542022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = -1.001542022 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = -1.001542022 + 1.944444445 x = -1.001542022 + 1.944444445 Combine like terms: -1.001542022 + 1.944444445 = 0.942902423 x = 0.942902423 Simplifying x = 0.942902423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.945986467, 0.942902423}
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