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Simplifying 5x2 + 20x + 0.1 = 0 Reorder the terms: 0.1 + 20x + 5x2 = 0 Solving 0.1 + 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'. 0.02 + 4x + x2 = 0 Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + 4x + -0.02 + x2 = 0 + -0.02 Reorder the terms: 0.02 + -0.02 + 4x + x2 = 0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + 4x + x2 = 0 + -0.02 4x + x2 = 0 + -0.02 Combine like terms: 0 + -0.02 = -0.02 4x + x2 = -0.02 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 = -0.02 + 4 Reorder the terms: 4 + 4x + x2 = -0.02 + 4 Combine like terms: -0.02 + 4 = 3.98 4 + 4x + x2 = 3.98 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.98 Calculate the square root of the right side: 1.994993734 Break this problem into two subproblems by setting (x + 2) equal to 1.994993734 and -1.994993734.Subproblem 1
x + 2 = 1.994993734 Simplifying x + 2 = 1.994993734 Reorder the terms: 2 + x = 1.994993734 Solving 2 + x = 1.994993734 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 = 1.994993734 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.994993734 + -2 x = 1.994993734 + -2 Combine like terms: 1.994993734 + -2 = -0.005006266 x = -0.005006266 Simplifying x = -0.005006266Subproblem 2
x + 2 = -1.994993734 Simplifying x + 2 = -1.994993734 Reorder the terms: 2 + x = -1.994993734 Solving 2 + x = -1.994993734 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 = -1.994993734 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.994993734 + -2 x = -1.994993734 + -2 Combine like terms: -1.994993734 + -2 = -3.994993734 x = -3.994993734 Simplifying x = -3.994993734Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.005006266, -3.994993734}
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