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Simplifying x2 + -9x + -84 = 0 Reorder the terms: -84 + -9x + x2 = 0 Solving -84 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -9x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -9x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -9x + x2 = 0 + 84 -9x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -9x + x2 = 84 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 = 84 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 84 + 20.25 Combine like terms: 84 + 20.25 = 104.25 20.25 + -9x + x2 = 104.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + -4.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + -4.5 = 10.210288928 Simplifying x + -4.5 = 10.210288928 Reorder the terms: -4.5 + x = 10.210288928 Solving -4.5 + x = 10.210288928 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 = 10.210288928 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 10.210288928 + 4.5 x = 10.210288928 + 4.5 Combine like terms: 10.210288928 + 4.5 = 14.710288928 x = 14.710288928 Simplifying x = 14.710288928Subproblem 2
x + -4.5 = -10.210288928 Simplifying x + -4.5 = -10.210288928 Reorder the terms: -4.5 + x = -10.210288928 Solving -4.5 + x = -10.210288928 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 = -10.210288928 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -10.210288928 + 4.5 x = -10.210288928 + 4.5 Combine like terms: -10.210288928 + 4.5 = -5.710288928 x = -5.710288928 Simplifying x = -5.710288928Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.710288928, -5.710288928}
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