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Simplifying x2 + -5x + -54 = 0 Reorder the terms: -54 + -5x + x2 = 0 Solving -54 + -5x + 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 + -5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -5x + x2 = 0 + 54 -5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -5x + x2 = 54 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 54 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 54 + 6.25 Combine like terms: 54 + 6.25 = 60.25 6.25 + -5x + x2 = 60.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -2.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -2.5 = 7.762087348 Simplifying x + -2.5 = 7.762087348 Reorder the terms: -2.5 + x = 7.762087348 Solving -2.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.762087348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.762087348 + 2.5 x = 7.762087348 + 2.5 Combine like terms: 7.762087348 + 2.5 = 10.262087348 x = 10.262087348 Simplifying x = 10.262087348Subproblem 2
x + -2.5 = -7.762087348 Simplifying x + -2.5 = -7.762087348 Reorder the terms: -2.5 + x = -7.762087348 Solving -2.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.762087348 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.762087348 + 2.5 x = -7.762087348 + 2.5 Combine like terms: -7.762087348 + 2.5 = -5.262087348 x = -5.262087348 Simplifying x = -5.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.262087348, -5.262087348}
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