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Simplifying 0 = x2 + 44x + -81 Reorder the terms: 0 = -81 + 44x + x2 Solving 0 = -81 + 44x + x2 Solving for variable 'x'. Combine like terms: 0 + 81 = 81 81 + -44x + -1x2 = -81 + 44x + x2 + 81 + -44x + -1x2 Reorder the terms: 81 + -44x + -1x2 = -81 + 81 + 44x + -44x + x2 + -1x2 Combine like terms: -81 + 81 = 0 81 + -44x + -1x2 = 0 + 44x + -44x + x2 + -1x2 81 + -44x + -1x2 = 44x + -44x + x2 + -1x2 Combine like terms: 44x + -44x = 0 81 + -44x + -1x2 = 0 + x2 + -1x2 81 + -44x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + -44x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + 44x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + 44x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 44x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 44x + x2 = 0 + 81 44x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 44x + x2 = 81 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = 81 + 484 Reorder the terms: 484 + 44x + x2 = 81 + 484 Combine like terms: 81 + 484 = 565 484 + 44x + x2 = 565 Factor a perfect square on the left side: (x + 22)(x + 22) = 565 Calculate the square root of the right side: 23.769728648 Break this problem into two subproblems by setting (x + 22) equal to 23.769728648 and -23.769728648.Subproblem 1
x + 22 = 23.769728648 Simplifying x + 22 = 23.769728648 Reorder the terms: 22 + x = 23.769728648 Solving 22 + x = 23.769728648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 23.769728648 + -22 Combine like terms: 22 + -22 = 0 0 + x = 23.769728648 + -22 x = 23.769728648 + -22 Combine like terms: 23.769728648 + -22 = 1.769728648 x = 1.769728648 Simplifying x = 1.769728648Subproblem 2
x + 22 = -23.769728648 Simplifying x + 22 = -23.769728648 Reorder the terms: 22 + x = -23.769728648 Solving 22 + x = -23.769728648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -23.769728648 + -22 Combine like terms: 22 + -22 = 0 0 + x = -23.769728648 + -22 x = -23.769728648 + -22 Combine like terms: -23.769728648 + -22 = -45.769728648 x = -45.769728648 Simplifying x = -45.769728648Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.769728648, -45.769728648}
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