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Simplifying X2 + 3.99X + -0.004 = 0 Reorder the terms: -0.004 + 3.99X + X2 = 0 Solving -0.004 + 3.99X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.004' to each side of the equation. -0.004 + 3.99X + 0.004 + X2 = 0 + 0.004 Reorder the terms: -0.004 + 0.004 + 3.99X + X2 = 0 + 0.004 Combine like terms: -0.004 + 0.004 = 0.000 0.000 + 3.99X + X2 = 0 + 0.004 3.99X + X2 = 0 + 0.004 Combine like terms: 0 + 0.004 = 0.004 3.99X + X2 = 0.004 The X term is 3.99X. Take half its coefficient (1.995). Square it (3.980025) and add it to both sides. Add '3.980025' to each side of the equation. 3.99X + 3.980025 + X2 = 0.004 + 3.980025 Reorder the terms: 3.980025 + 3.99X + X2 = 0.004 + 3.980025 Combine like terms: 0.004 + 3.980025 = 3.984025 3.980025 + 3.99X + X2 = 3.984025 Factor a perfect square on the left side: (X + 1.995)(X + 1.995) = 3.984025 Calculate the square root of the right side: 1.996002255 Break this problem into two subproblems by setting (X + 1.995) equal to 1.996002255 and -1.996002255.Subproblem 1
X + 1.995 = 1.996002255 Simplifying X + 1.995 = 1.996002255 Reorder the terms: 1.995 + X = 1.996002255 Solving 1.995 + X = 1.996002255 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.995' to each side of the equation. 1.995 + -1.995 + X = 1.996002255 + -1.995 Combine like terms: 1.995 + -1.995 = 0.000 0.000 + X = 1.996002255 + -1.995 X = 1.996002255 + -1.995 Combine like terms: 1.996002255 + -1.995 = 0.001002255 X = 0.001002255 Simplifying X = 0.001002255Subproblem 2
X + 1.995 = -1.996002255 Simplifying X + 1.995 = -1.996002255 Reorder the terms: 1.995 + X = -1.996002255 Solving 1.995 + X = -1.996002255 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.995' to each side of the equation. 1.995 + -1.995 + X = -1.996002255 + -1.995 Combine like terms: 1.995 + -1.995 = 0.000 0.000 + X = -1.996002255 + -1.995 X = -1.996002255 + -1.995 Combine like terms: -1.996002255 + -1.995 = -3.991002255 X = -3.991002255 Simplifying X = -3.991002255Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.001002255, -3.991002255}
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