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Simplifying x2 + -99x + -54 = 0 Reorder the terms: -54 + -99x + x2 = 0 Solving -54 + -99x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -99x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -99x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -99x + x2 = 0 + 54 -99x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -99x + x2 = 54 The x term is -99x. Take half its coefficient (-49.5). Square it (2450.25) and add it to both sides. Add '2450.25' to each side of the equation. -99x + 2450.25 + x2 = 54 + 2450.25 Reorder the terms: 2450.25 + -99x + x2 = 54 + 2450.25 Combine like terms: 54 + 2450.25 = 2504.25 2450.25 + -99x + x2 = 2504.25 Factor a perfect square on the left side: (x + -49.5)(x + -49.5) = 2504.25 Calculate the square root of the right side: 50.042481953 Break this problem into two subproblems by setting (x + -49.5) equal to 50.042481953 and -50.042481953.Subproblem 1
x + -49.5 = 50.042481953 Simplifying x + -49.5 = 50.042481953 Reorder the terms: -49.5 + x = 50.042481953 Solving -49.5 + x = 50.042481953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.5' to each side of the equation. -49.5 + 49.5 + x = 50.042481953 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + x = 50.042481953 + 49.5 x = 50.042481953 + 49.5 Combine like terms: 50.042481953 + 49.5 = 99.542481953 x = 99.542481953 Simplifying x = 99.542481953Subproblem 2
x + -49.5 = -50.042481953 Simplifying x + -49.5 = -50.042481953 Reorder the terms: -49.5 + x = -50.042481953 Solving -49.5 + x = -50.042481953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49.5' to each side of the equation. -49.5 + 49.5 + x = -50.042481953 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + x = -50.042481953 + 49.5 x = -50.042481953 + 49.5 Combine like terms: -50.042481953 + 49.5 = -0.542481953 x = -0.542481953 Simplifying x = -0.542481953Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.542481953, -0.542481953}
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