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Simplifying 5X2 + 20X + 1 = 0 Reorder the terms: 1 + 20X + 5X2 = 0 Solving 1 + 20X + 5X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 4X + X2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 4X + -0.2 + X2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 4X + X2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 4X + X2 = 0 + -0.2 4X + X2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 4X + X2 = -0.2 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = -0.2 + 4 Reorder the terms: 4 + 4X + X2 = -0.2 + 4 Combine like terms: -0.2 + 4 = 3.8 4 + 4X + X2 = 3.8 Factor a perfect square on the left side: (X + 2)(X + 2) = 3.8 Calculate the square root of the right side: 1.949358869 Break this problem into two subproblems by setting (X + 2) equal to 1.949358869 and -1.949358869.Subproblem 1
X + 2 = 1.949358869 Simplifying X + 2 = 1.949358869 Reorder the terms: 2 + X = 1.949358869 Solving 2 + X = 1.949358869 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 1.949358869 + -2 Combine like terms: 2 + -2 = 0 0 + X = 1.949358869 + -2 X = 1.949358869 + -2 Combine like terms: 1.949358869 + -2 = -0.050641131 X = -0.050641131 Simplifying X = -0.050641131Subproblem 2
X + 2 = -1.949358869 Simplifying X + 2 = -1.949358869 Reorder the terms: 2 + X = -1.949358869 Solving 2 + X = -1.949358869 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -1.949358869 + -2 Combine like terms: 2 + -2 = 0 0 + X = -1.949358869 + -2 X = -1.949358869 + -2 Combine like terms: -1.949358869 + -2 = -3.949358869 X = -3.949358869 Simplifying X = -3.949358869Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.050641131, -3.949358869}
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