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Simplifying -1x2 + -113x + 22 = 0 Reorder the terms: 22 + -113x + -1x2 = 0 Solving 22 + -113x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + 113x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 113x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 113x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 113x + x2 = 0 + 22 113x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 113x + x2 = 22 The x term is 113x. Take half its coefficient (56.5). Square it (3192.25) and add it to both sides. Add '3192.25' to each side of the equation. 113x + 3192.25 + x2 = 22 + 3192.25 Reorder the terms: 3192.25 + 113x + x2 = 22 + 3192.25 Combine like terms: 22 + 3192.25 = 3214.25 3192.25 + 113x + x2 = 3214.25 Factor a perfect square on the left side: (x + 56.5)(x + 56.5) = 3214.25 Calculate the square root of the right side: 56.69435598 Break this problem into two subproblems by setting (x + 56.5) equal to 56.69435598 and -56.69435598.Subproblem 1
x + 56.5 = 56.69435598 Simplifying x + 56.5 = 56.69435598 Reorder the terms: 56.5 + x = 56.69435598 Solving 56.5 + x = 56.69435598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56.5' to each side of the equation. 56.5 + -56.5 + x = 56.69435598 + -56.5 Combine like terms: 56.5 + -56.5 = 0.0 0.0 + x = 56.69435598 + -56.5 x = 56.69435598 + -56.5 Combine like terms: 56.69435598 + -56.5 = 0.19435598 x = 0.19435598 Simplifying x = 0.19435598Subproblem 2
x + 56.5 = -56.69435598 Simplifying x + 56.5 = -56.69435598 Reorder the terms: 56.5 + x = -56.69435598 Solving 56.5 + x = -56.69435598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56.5' to each side of the equation. 56.5 + -56.5 + x = -56.69435598 + -56.5 Combine like terms: 56.5 + -56.5 = 0.0 0.0 + x = -56.69435598 + -56.5 x = -56.69435598 + -56.5 Combine like terms: -56.69435598 + -56.5 = -113.19435598 x = -113.19435598 Simplifying x = -113.19435598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19435598, -113.19435598}
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