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Simplifying 121 = 110x + -1x2 Solving 121 = 110x + -1x2 Solving for variable 'x'. Reorder the terms: 121 + -110x + x2 = 110x + -110x + -1x2 + x2 Combine like terms: 110x + -110x = 0 121 + -110x + x2 = 0 + -1x2 + x2 121 + -110x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 121 + -110x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-121' to each side of the equation. 121 + -110x + -121 + x2 = 0 + -121 Reorder the terms: 121 + -121 + -110x + x2 = 0 + -121 Combine like terms: 121 + -121 = 0 0 + -110x + x2 = 0 + -121 -110x + x2 = 0 + -121 Combine like terms: 0 + -121 = -121 -110x + x2 = -121 The x term is -110x. Take half its coefficient (-55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. -110x + 3025 + x2 = -121 + 3025 Reorder the terms: 3025 + -110x + x2 = -121 + 3025 Combine like terms: -121 + 3025 = 2904 3025 + -110x + x2 = 2904 Factor a perfect square on the left side: (x + -55)(x + -55) = 2904 Calculate the square root of the right side: 53.888774341 Break this problem into two subproblems by setting (x + -55) equal to 53.888774341 and -53.888774341.Subproblem 1
x + -55 = 53.888774341 Simplifying x + -55 = 53.888774341 Reorder the terms: -55 + x = 53.888774341 Solving -55 + x = 53.888774341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = 53.888774341 + 55 Combine like terms: -55 + 55 = 0 0 + x = 53.888774341 + 55 x = 53.888774341 + 55 Combine like terms: 53.888774341 + 55 = 108.888774341 x = 108.888774341 Simplifying x = 108.888774341Subproblem 2
x + -55 = -53.888774341 Simplifying x + -55 = -53.888774341 Reorder the terms: -55 + x = -53.888774341 Solving -55 + x = -53.888774341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = -53.888774341 + 55 Combine like terms: -55 + 55 = 0 0 + x = -53.888774341 + 55 x = -53.888774341 + 55 Combine like terms: -53.888774341 + 55 = 1.111225659 x = 1.111225659 Simplifying x = 1.111225659Solution
The solution to the problem is based on the solutions from the subproblems. x = {108.888774341, 1.111225659}
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