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Simplifying X2 + 9X + -64 = 0 Reorder the terms: -64 + 9X + X2 = 0 Solving -64 + 9X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 9X + 64 + X2 = 0 + 64 Reorder the terms: -64 + 64 + 9X + X2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 9X + X2 = 0 + 64 9X + X2 = 0 + 64 Combine like terms: 0 + 64 = 64 9X + X2 = 64 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 = 64 + 20.25 Reorder the terms: 20.25 + 9X + X2 = 64 + 20.25 Combine like terms: 64 + 20.25 = 84.25 20.25 + 9X + X2 = 84.25 Factor a perfect square on the left side: (X + 4.5)(X + 4.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (X + 4.5) equal to 9.178779875 and -9.178779875.Subproblem 1
X + 4.5 = 9.178779875 Simplifying X + 4.5 = 9.178779875 Reorder the terms: 4.5 + X = 9.178779875 Solving 4.5 + X = 9.178779875 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 = 9.178779875 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = 9.178779875 + -4.5 X = 9.178779875 + -4.5 Combine like terms: 9.178779875 + -4.5 = 4.678779875 X = 4.678779875 Simplifying X = 4.678779875Subproblem 2
X + 4.5 = -9.178779875 Simplifying X + 4.5 = -9.178779875 Reorder the terms: 4.5 + X = -9.178779875 Solving 4.5 + X = -9.178779875 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 = -9.178779875 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = -9.178779875 + -4.5 X = -9.178779875 + -4.5 Combine like terms: -9.178779875 + -4.5 = -13.678779875 X = -13.678779875 Simplifying X = -13.678779875Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.678779875, -13.678779875}
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