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Simplifying 9X2 + 38X + 25 = 0 Reorder the terms: 25 + 38X + 9X2 = 0 Solving 25 + 38X + 9X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.777777778 + 4.222222222X + X2 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + 4.222222222X + -2.777777778 + X2 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + 4.222222222X + X2 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + 4.222222222X + X2 = 0 + -2.777777778 4.222222222X + X2 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 4.222222222X + X2 = -2.777777778 The X term is 4.222222222X. Take half its coefficient (2.111111111). Square it (4.456790123) and add it to both sides. Add '4.456790123' to each side of the equation. 4.222222222X + 4.456790123 + X2 = -2.777777778 + 4.456790123 Reorder the terms: 4.456790123 + 4.222222222X + X2 = -2.777777778 + 4.456790123 Combine like terms: -2.777777778 + 4.456790123 = 1.679012345 4.456790123 + 4.222222222X + X2 = 1.679012345 Factor a perfect square on the left side: (X + 2.111111111)(X + 2.111111111) = 1.679012345 Calculate the square root of the right side: 1.295767087 Break this problem into two subproblems by setting (X + 2.111111111) equal to 1.295767087 and -1.295767087.Subproblem 1
X + 2.111111111 = 1.295767087 Simplifying X + 2.111111111 = 1.295767087 Reorder the terms: 2.111111111 + X = 1.295767087 Solving 2.111111111 + X = 1.295767087 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.111111111' to each side of the equation. 2.111111111 + -2.111111111 + X = 1.295767087 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + X = 1.295767087 + -2.111111111 X = 1.295767087 + -2.111111111 Combine like terms: 1.295767087 + -2.111111111 = -0.815344024 X = -0.815344024 Simplifying X = -0.815344024Subproblem 2
X + 2.111111111 = -1.295767087 Simplifying X + 2.111111111 = -1.295767087 Reorder the terms: 2.111111111 + X = -1.295767087 Solving 2.111111111 + X = -1.295767087 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.111111111' to each side of the equation. 2.111111111 + -2.111111111 + X = -1.295767087 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + X = -1.295767087 + -2.111111111 X = -1.295767087 + -2.111111111 Combine like terms: -1.295767087 + -2.111111111 = -3.406878198 X = -3.406878198 Simplifying X = -3.406878198Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.815344024, -3.406878198}
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