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Simplifying X2 + -60X + 20 = 0 Reorder the terms: 20 + -60X + X2 = 0 Solving 20 + -60X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -60X + -20 + X2 = 0 + -20 Reorder the terms: 20 + -20 + -60X + X2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -60X + X2 = 0 + -20 -60X + X2 = 0 + -20 Combine like terms: 0 + -20 = -20 -60X + X2 = -20 The X term is -60X. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60X + 900 + X2 = -20 + 900 Reorder the terms: 900 + -60X + X2 = -20 + 900 Combine like terms: -20 + 900 = 880 900 + -60X + X2 = 880 Factor a perfect square on the left side: (X + -30)(X + -30) = 880 Calculate the square root of the right side: 29.664793948 Break this problem into two subproblems by setting (X + -30) equal to 29.664793948 and -29.664793948.Subproblem 1
X + -30 = 29.664793948 Simplifying X + -30 = 29.664793948 Reorder the terms: -30 + X = 29.664793948 Solving -30 + X = 29.664793948 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + X = 29.664793948 + 30 Combine like terms: -30 + 30 = 0 0 + X = 29.664793948 + 30 X = 29.664793948 + 30 Combine like terms: 29.664793948 + 30 = 59.664793948 X = 59.664793948 Simplifying X = 59.664793948Subproblem 2
X + -30 = -29.664793948 Simplifying X + -30 = -29.664793948 Reorder the terms: -30 + X = -29.664793948 Solving -30 + X = -29.664793948 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + X = -29.664793948 + 30 Combine like terms: -30 + 30 = 0 0 + X = -29.664793948 + 30 X = -29.664793948 + 30 Combine like terms: -29.664793948 + 30 = 0.335206052 X = 0.335206052 Simplifying X = 0.335206052Solution
The solution to the problem is based on the solutions from the subproblems. X = {59.664793948, 0.335206052}
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