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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 = -0.629171307 x = -0.629171307 Simplifying x = -0.629171307Subproblem 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 = -4.370828693 x = -4.370828693 Simplifying x = -4.370828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.629171307, -4.370828693}
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