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Simplifying 2x2 + 11x + -42 = 0 Reorder the terms: -42 + 11x + 2x2 = 0 Solving -42 + 11x + 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'. -21 + 5.5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 5.5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 5.5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 5.5x + x2 = 0 + 21 5.5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 5.5x + x2 = 21 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 21 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 21 + 7.5625 Combine like terms: 21 + 7.5625 = 28.5625 7.5625 + 5.5x + x2 = 28.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 28.5625 Calculate the square root of the right side: 5.344389582 Break this problem into two subproblems by setting (x + 2.75) equal to 5.344389582 and -5.344389582.Subproblem 1
x + 2.75 = 5.344389582 Simplifying x + 2.75 = 5.344389582 Reorder the terms: 2.75 + x = 5.344389582 Solving 2.75 + x = 5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 5.344389582 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 5.344389582 + -2.75 x = 5.344389582 + -2.75 Combine like terms: 5.344389582 + -2.75 = 2.594389582 x = 2.594389582 Simplifying x = 2.594389582Subproblem 2
x + 2.75 = -5.344389582 Simplifying x + 2.75 = -5.344389582 Reorder the terms: 2.75 + x = -5.344389582 Solving 2.75 + x = -5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -5.344389582 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -5.344389582 + -2.75 x = -5.344389582 + -2.75 Combine like terms: -5.344389582 + -2.75 = -8.094389582 x = -8.094389582 Simplifying x = -8.094389582Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.594389582, -8.094389582}
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