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Simplifying 2x2 + -22x + -73 = 0 Reorder the terms: -73 + -22x + 2x2 = 0 Solving -73 + -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'. -36.5 + -11x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + -11x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + -11x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + -11x + x2 = 0 + 36.5 -11x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 -11x + x2 = 36.5 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 = 36.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 36.5 + 30.25 Combine like terms: 36.5 + 30.25 = 66.75 30.25 + -11x + x2 = 66.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 66.75 Calculate the square root of the right side: 8.170067319 Break this problem into two subproblems by setting (x + -5.5) equal to 8.170067319 and -8.170067319.Subproblem 1
x + -5.5 = 8.170067319 Simplifying x + -5.5 = 8.170067319 Reorder the terms: -5.5 + x = 8.170067319 Solving -5.5 + x = 8.170067319 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 = 8.170067319 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.170067319 + 5.5 x = 8.170067319 + 5.5 Combine like terms: 8.170067319 + 5.5 = 13.670067319 x = 13.670067319 Simplifying x = 13.670067319Subproblem 2
x + -5.5 = -8.170067319 Simplifying x + -5.5 = -8.170067319 Reorder the terms: -5.5 + x = -8.170067319 Solving -5.5 + x = -8.170067319 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 = -8.170067319 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.170067319 + 5.5 x = -8.170067319 + 5.5 Combine like terms: -8.170067319 + 5.5 = -2.670067319 x = -2.670067319 Simplifying x = -2.670067319Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.670067319, -2.670067319}
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