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Simplifying (4x2) + -20x + 11 = 0 Reorder the terms: 11 + -20x + (4x2) = 0 Solving 11 + -20x + (4x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + -5x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -5x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -5x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -5x + x2 = 0 + -2.75 -5x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -5x + x2 = -2.75 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 = -2.75 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2.75 + 6.25 Combine like terms: -2.75 + 6.25 = 3.5 6.25 + -5x + x2 = 3.5 Factor a perfect square on the left side: ((x) + -2.5)((x) + -2.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting ((x) + -2.5) equal to 1.870828693 and -1.870828693.Subproblem 1
(x) + -2.5 = 1.870828693 Simplifying (x) + -2.5 = 1.870828693 x + -2.5 = 1.870828693 Reorder the terms: -2.5 + x = 1.870828693 Solving -2.5 + x = 1.870828693 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 = 1.870828693 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.870828693 + 2.5 x = 1.870828693 + 2.5 Combine like terms: 1.870828693 + 2.5 = 4.370828693 x = 4.370828693 Simplifying x = 4.370828693Subproblem 2
(x) + -2.5 = -1.870828693 Simplifying (x) + -2.5 = -1.870828693 x + -2.5 = -1.870828693 Reorder the terms: -2.5 + x = -1.870828693 Solving -2.5 + x = -1.870828693 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 = -1.870828693 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.870828693 + 2.5 x = -1.870828693 + 2.5 Combine like terms: -1.870828693 + 2.5 = 0.629171307 x = 0.629171307 Simplifying x = 0.629171307Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.370828693, 0.629171307}
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