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Simplifying x2 + -110x + 195 = 0 Reorder the terms: 195 + -110x + x2 = 0 Solving 195 + -110x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-195' to each side of the equation. 195 + -110x + -195 + x2 = 0 + -195 Reorder the terms: 195 + -195 + -110x + x2 = 0 + -195 Combine like terms: 195 + -195 = 0 0 + -110x + x2 = 0 + -195 -110x + x2 = 0 + -195 Combine like terms: 0 + -195 = -195 -110x + x2 = -195 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 = -195 + 3025 Reorder the terms: 3025 + -110x + x2 = -195 + 3025 Combine like terms: -195 + 3025 = 2830 3025 + -110x + x2 = 2830 Factor a perfect square on the left side: (x + -55)(x + -55) = 2830 Calculate the square root of the right side: 53.197744313 Break this problem into two subproblems by setting (x + -55) equal to 53.197744313 and -53.197744313.Subproblem 1
x + -55 = 53.197744313 Simplifying x + -55 = 53.197744313 Reorder the terms: -55 + x = 53.197744313 Solving -55 + x = 53.197744313 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 = 53.197744313 + 55 Combine like terms: -55 + 55 = 0 0 + x = 53.197744313 + 55 x = 53.197744313 + 55 Combine like terms: 53.197744313 + 55 = 108.197744313 x = 108.197744313 Simplifying x = 108.197744313Subproblem 2
x + -55 = -53.197744313 Simplifying x + -55 = -53.197744313 Reorder the terms: -55 + x = -53.197744313 Solving -55 + x = -53.197744313 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 = -53.197744313 + 55 Combine like terms: -55 + 55 = 0 0 + x = -53.197744313 + 55 x = -53.197744313 + 55 Combine like terms: -53.197744313 + 55 = 1.802255687 x = 1.802255687 Simplifying x = 1.802255687Solution
The solution to the problem is based on the solutions from the subproblems. x = {108.197744313, 1.802255687}
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