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Simplifying 20x2 + -20x + -11 = 0 Reorder the terms: -11 + -20x + 20x2 = 0 Solving -11 + -20x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.55 + -1x + x2 = 0 Move the constant term to the right: Add '0.55' to each side of the equation. -0.55 + -1x + 0.55 + x2 = 0 + 0.55 Reorder the terms: -0.55 + 0.55 + -1x + x2 = 0 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + -1x + x2 = 0 + 0.55 -1x + x2 = 0 + 0.55 Combine like terms: 0 + 0.55 = 0.55 -1x + x2 = 0.55 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.55 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.55 + 0.25 Combine like terms: 0.55 + 0.25 = 0.8 0.25 + -1x + x2 = 0.8 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (x + -0.5) equal to 0.894427191 and -0.894427191.Subproblem 1
x + -0.5 = 0.894427191 Simplifying x + -0.5 = 0.894427191 Reorder the terms: -0.5 + x = 0.894427191 Solving -0.5 + x = 0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.894427191 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.894427191 + 0.5 x = 0.894427191 + 0.5 Combine like terms: 0.894427191 + 0.5 = 1.394427191 x = 1.394427191 Simplifying x = 1.394427191Subproblem 2
x + -0.5 = -0.894427191 Simplifying x + -0.5 = -0.894427191 Reorder the terms: -0.5 + x = -0.894427191 Solving -0.5 + x = -0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.894427191 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.894427191 + 0.5 x = -0.894427191 + 0.5 Combine like terms: -0.894427191 + 0.5 = -0.394427191 x = -0.394427191 Simplifying x = -0.394427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.394427191, -0.394427191}
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