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Simplifying 2x2 + -10x + 11 = 0 Reorder the terms: 11 + -10x + 2x2 = 0 Solving 11 + -10x + 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 + -5x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -5x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -5x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -5x + x2 = 0 + -5.5 -5x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -5x + x2 = -5.5 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 = -5.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -5.5 + 6.25 Combine like terms: -5.5 + 6.25 = 0.75 6.25 + -5x + x2 = 0.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -2.5) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -2.5 = 0.866025404 Simplifying x + -2.5 = 0.866025404 Reorder the terms: -2.5 + x = 0.866025404 Solving -2.5 + x = 0.866025404 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 = 0.866025404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 0.866025404 + 2.5 x = 0.866025404 + 2.5 Combine like terms: 0.866025404 + 2.5 = 3.366025404 x = 3.366025404 Simplifying x = 3.366025404Subproblem 2
x + -2.5 = -0.866025404 Simplifying x + -2.5 = -0.866025404 Reorder the terms: -2.5 + x = -0.866025404 Solving -2.5 + x = -0.866025404 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 = -0.866025404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -0.866025404 + 2.5 x = -0.866025404 + 2.5 Combine like terms: -0.866025404 + 2.5 = 1.633974596 x = 1.633974596 Simplifying x = 1.633974596Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.366025404, 1.633974596}
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