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Simplifying X2 + -9X + -30 = 0 Reorder the terms: -30 + -9X + X2 = 0 Solving -30 + -9X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -9X + 30 + X2 = 0 + 30 Reorder the terms: -30 + 30 + -9X + X2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -9X + X2 = 0 + 30 -9X + X2 = 0 + 30 Combine like terms: 0 + 30 = 30 -9X + X2 = 30 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 = 30 + 20.25 Reorder the terms: 20.25 + -9X + X2 = 30 + 20.25 Combine like terms: 30 + 20.25 = 50.25 20.25 + -9X + X2 = 50.25 Factor a perfect square on the left side: (X + -4.5)(X + -4.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (X + -4.5) equal to 7.088723439 and -7.088723439.Subproblem 1
X + -4.5 = 7.088723439 Simplifying X + -4.5 = 7.088723439 Reorder the terms: -4.5 + X = 7.088723439 Solving -4.5 + X = 7.088723439 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 = 7.088723439 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = 7.088723439 + 4.5 X = 7.088723439 + 4.5 Combine like terms: 7.088723439 + 4.5 = 11.588723439 X = 11.588723439 Simplifying X = 11.588723439Subproblem 2
X + -4.5 = -7.088723439 Simplifying X + -4.5 = -7.088723439 Reorder the terms: -4.5 + X = -7.088723439 Solving -4.5 + X = -7.088723439 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 = -7.088723439 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = -7.088723439 + 4.5 X = -7.088723439 + 4.5 Combine like terms: -7.088723439 + 4.5 = -2.588723439 X = -2.588723439 Simplifying X = -2.588723439Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.588723439, -2.588723439}
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