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Simplifying 2x2 + 20x + 11 = 0 Reorder the terms: 11 + 20x + 2x2 = 0 Solving 11 + 20x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 10x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 10x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 10x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 10x + x2 = 0 + -5.5 10x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 10x + x2 = -5.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -5.5 + 25 Reorder the terms: 25 + 10x + x2 = -5.5 + 25 Combine like terms: -5.5 + 25 = 19.5 25 + 10x + x2 = 19.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + 5) equal to 4.415880433 and -4.415880433.Subproblem 1
x + 5 = 4.415880433 Simplifying x + 5 = 4.415880433 Reorder the terms: 5 + x = 4.415880433 Solving 5 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.415880433 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.415880433 + -5 x = 4.415880433 + -5 Combine like terms: 4.415880433 + -5 = -0.584119567 x = -0.584119567 Simplifying x = -0.584119567Subproblem 2
x + 5 = -4.415880433 Simplifying x + 5 = -4.415880433 Reorder the terms: 5 + x = -4.415880433 Solving 5 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.415880433 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.415880433 + -5 x = -4.415880433 + -5 Combine like terms: -4.415880433 + -5 = -9.415880433 x = -9.415880433 Simplifying x = -9.415880433Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.584119567, -9.415880433}
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