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Simplifying 5x2 + -25x + 9 = 0 Reorder the terms: 9 + -25x + 5x2 = 0 Solving 9 + -25x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -5x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -5x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -5x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -5x + x2 = 0 + -1.8 -5x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -5x + x2 = -1.8 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 = -1.8 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.8 + 6.25 Combine like terms: -1.8 + 6.25 = 4.45 6.25 + -5x + x2 = 4.45 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.45 Calculate the square root of the right side: 2.109502311 Break this problem into two subproblems by setting (x + -2.5) equal to 2.109502311 and -2.109502311.Subproblem 1
x + -2.5 = 2.109502311 Simplifying x + -2.5 = 2.109502311 Reorder the terms: -2.5 + x = 2.109502311 Solving -2.5 + x = 2.109502311 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 = 2.109502311 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.109502311 + 2.5 x = 2.109502311 + 2.5 Combine like terms: 2.109502311 + 2.5 = 4.609502311 x = 4.609502311 Simplifying x = 4.609502311Subproblem 2
x + -2.5 = -2.109502311 Simplifying x + -2.5 = -2.109502311 Reorder the terms: -2.5 + x = -2.109502311 Solving -2.5 + x = -2.109502311 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 = -2.109502311 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.109502311 + 2.5 x = -2.109502311 + 2.5 Combine like terms: -2.109502311 + 2.5 = 0.390497689 x = 0.390497689 Simplifying x = 0.390497689Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.609502311, 0.390497689}
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