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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 = -3.291796067 x = -3.291796067 Simplifying x = -3.291796067Subproblem 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 = -16.708203933 x = -16.708203933 Simplifying x = -16.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.291796067, -16.708203933}
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