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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 = 4.11684397 x = 4.11684397 Simplifying x = 4.11684397Subproblem 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 = -13.11684397 x = -13.11684397 Simplifying x = -13.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.11684397, -13.11684397}
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