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Simplifying x2 + -9x + -54 = 0 Reorder the terms: -54 + -9x + x2 = 0 Solving -54 + -9x + 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 + -9x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -9x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -9x + x2 = 0 + 54 -9x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -9x + x2 = 54 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 54 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 54 + 20.25 Combine like terms: 54 + 20.25 = 74.25 20.25 + -9x + x2 = 74.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + -4.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + -4.5 = 8.61684397 Simplifying x + -4.5 = 8.61684397 Reorder the terms: -4.5 + x = 8.61684397 Solving -4.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 8.61684397 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 8.61684397 + 4.5 x = 8.61684397 + 4.5 Combine like terms: 8.61684397 + 4.5 = 13.11684397 x = 13.11684397 Simplifying x = 13.11684397Subproblem 2
x + -4.5 = -8.61684397 Simplifying x + -4.5 = -8.61684397 Reorder the terms: -4.5 + x = -8.61684397 Solving -4.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -8.61684397 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -8.61684397 + 4.5 x = -8.61684397 + 4.5 Combine like terms: -8.61684397 + 4.5 = -4.11684397 x = -4.11684397 Simplifying x = -4.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.11684397, -4.11684397}
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