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Simplifying -1x2 + 9x + 321 = 0 Reorder the terms: 321 + 9x + -1x2 = 0 Solving 321 + 9x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -321 + -9x + x2 = 0 Move the constant term to the right: Add '321' to each side of the equation. -321 + -9x + 321 + x2 = 0 + 321 Reorder the terms: -321 + 321 + -9x + x2 = 0 + 321 Combine like terms: -321 + 321 = 0 0 + -9x + x2 = 0 + 321 -9x + x2 = 0 + 321 Combine like terms: 0 + 321 = 321 -9x + x2 = 321 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 = 321 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 321 + 20.25 Combine like terms: 321 + 20.25 = 341.25 20.25 + -9x + x2 = 341.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 341.25 Calculate the square root of the right side: 18.472953202 Break this problem into two subproblems by setting (x + -4.5) equal to 18.472953202 and -18.472953202.Subproblem 1
x + -4.5 = 18.472953202 Simplifying x + -4.5 = 18.472953202 Reorder the terms: -4.5 + x = 18.472953202 Solving -4.5 + x = 18.472953202 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 = 18.472953202 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 18.472953202 + 4.5 x = 18.472953202 + 4.5 Combine like terms: 18.472953202 + 4.5 = 22.972953202 x = 22.972953202 Simplifying x = 22.972953202Subproblem 2
x + -4.5 = -18.472953202 Simplifying x + -4.5 = -18.472953202 Reorder the terms: -4.5 + x = -18.472953202 Solving -4.5 + x = -18.472953202 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 = -18.472953202 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -18.472953202 + 4.5 x = -18.472953202 + 4.5 Combine like terms: -18.472953202 + 4.5 = -13.972953202 x = -13.972953202 Simplifying x = -13.972953202Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.972953202, -13.972953202}
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