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Simplifying 9x2 + -45x + 17 = 0 Reorder the terms: 17 + -45x + 9x2 = 0 Solving 17 + -45x + 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'. 1.888888889 + -5x + x2 = 0 Move the constant term to the right: Add '-1.888888889' to each side of the equation. 1.888888889 + -5x + -1.888888889 + x2 = 0 + -1.888888889 Reorder the terms: 1.888888889 + -1.888888889 + -5x + x2 = 0 + -1.888888889 Combine like terms: 1.888888889 + -1.888888889 = 0.000000000 0.000000000 + -5x + x2 = 0 + -1.888888889 -5x + x2 = 0 + -1.888888889 Combine like terms: 0 + -1.888888889 = -1.888888889 -5x + x2 = -1.888888889 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1.888888889 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.888888889 + 6.25 Combine like terms: -1.888888889 + 6.25 = 4.361111111 6.25 + -5x + x2 = 4.361111111 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.361111111 Calculate the square root of the right side: 2.088327348 Break this problem into two subproblems by setting (x + -2.5) equal to 2.088327348 and -2.088327348.Subproblem 1
x + -2.5 = 2.088327348 Simplifying x + -2.5 = 2.088327348 Reorder the terms: -2.5 + x = 2.088327348 Solving -2.5 + x = 2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.088327348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.088327348 + 2.5 x = 2.088327348 + 2.5 Combine like terms: 2.088327348 + 2.5 = 4.588327348 x = 4.588327348 Simplifying x = 4.588327348Subproblem 2
x + -2.5 = -2.088327348 Simplifying x + -2.5 = -2.088327348 Reorder the terms: -2.5 + x = -2.088327348 Solving -2.5 + x = -2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.088327348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.088327348 + 2.5 x = -2.088327348 + 2.5 Combine like terms: -2.088327348 + 2.5 = 0.411672652 x = 0.411672652 Simplifying x = 0.411672652Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.588327348, 0.411672652}
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