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Simplifying 2x2 + -22x + 59 = 0 Reorder the terms: 59 + -22x + 2x2 = 0 Solving 59 + -22x + 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'. 29.5 + -11x + x2 = 0 Move the constant term to the right: Add '-29.5' to each side of the equation. 29.5 + -11x + -29.5 + x2 = 0 + -29.5 Reorder the terms: 29.5 + -29.5 + -11x + x2 = 0 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + -11x + x2 = 0 + -29.5 -11x + x2 = 0 + -29.5 Combine like terms: 0 + -29.5 = -29.5 -11x + x2 = -29.5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -29.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -29.5 + 30.25 Combine like terms: -29.5 + 30.25 = 0.75 30.25 + -11x + x2 = 0.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -5.5) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -5.5 = 0.866025404 Simplifying x + -5.5 = 0.866025404 Reorder the terms: -5.5 + x = 0.866025404 Solving -5.5 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 0.866025404 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.866025404 + 5.5 x = 0.866025404 + 5.5 Combine like terms: 0.866025404 + 5.5 = 6.366025404 x = 6.366025404 Simplifying x = 6.366025404Subproblem 2
x + -5.5 = -0.866025404 Simplifying x + -5.5 = -0.866025404 Reorder the terms: -5.5 + x = -0.866025404 Solving -5.5 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -0.866025404 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -0.866025404 + 5.5 x = -0.866025404 + 5.5 Combine like terms: -0.866025404 + 5.5 = 4.633974596 x = 4.633974596 Simplifying x = 4.633974596Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.366025404, 4.633974596}
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