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Simplifying x2 + -20x + 55 = 0 Reorder the terms: 55 + -20x + x2 = 0 Solving 55 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + -20x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + -20x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -20x + x2 = 0 + -55 -20x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 -20x + x2 = -55 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -55 + 100 Reorder the terms: 100 + -20x + x2 = -55 + 100 Combine like terms: -55 + 100 = 45 100 + -20x + x2 = 45 Factor a perfect square on the left side: (x + -10)(x + -10) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -10) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -10 = 6.708203933 Simplifying x + -10 = 6.708203933 Reorder the terms: -10 + x = 6.708203933 Solving -10 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 6.708203933 + 10 Combine like terms: -10 + 10 = 0 0 + x = 6.708203933 + 10 x = 6.708203933 + 10 Combine like terms: 6.708203933 + 10 = 16.708203933 x = 16.708203933 Simplifying x = 16.708203933Subproblem 2
x + -10 = -6.708203933 Simplifying x + -10 = -6.708203933 Reorder the terms: -10 + x = -6.708203933 Solving -10 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -6.708203933 + 10 Combine like terms: -10 + 10 = 0 0 + x = -6.708203933 + 10 x = -6.708203933 + 10 Combine like terms: -6.708203933 + 10 = 3.291796067 x = 3.291796067 Simplifying x = 3.291796067Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.708203933, 3.291796067}
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