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Simplifying x2 + 3x + 0.4 = 0.1 Reorder the terms: 0.4 + 3x + x2 = 0.1 Solving 0.4 + 3x + x2 = 0.1 Solving for variable 'x'. Reorder the terms: 0.4 + -0.1 + 3x + x2 = 0.1 + -0.1 Combine like terms: 0.4 + -0.1 = 0.3 0.3 + 3x + x2 = 0.1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.3 + 3x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + 3x + -0.3 + x2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + 3x + x2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + 3x + x2 = 0.0 + -0.3 3x + x2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 3x + x2 = -0.3 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -0.3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.3 + 2.25 Combine like terms: -0.3 + 2.25 = 1.95 2.25 + 3x + x2 = 1.95 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.95 Calculate the square root of the right side: 1.396424004 Break this problem into two subproblems by setting (x + 1.5) equal to 1.396424004 and -1.396424004.Subproblem 1
x + 1.5 = 1.396424004 Simplifying x + 1.5 = 1.396424004 Reorder the terms: 1.5 + x = 1.396424004 Solving 1.5 + x = 1.396424004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.396424004 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.396424004 + -1.5 x = 1.396424004 + -1.5 Combine like terms: 1.396424004 + -1.5 = -0.103575996 x = -0.103575996 Simplifying x = -0.103575996Subproblem 2
x + 1.5 = -1.396424004 Simplifying x + 1.5 = -1.396424004 Reorder the terms: 1.5 + x = -1.396424004 Solving 1.5 + x = -1.396424004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.396424004 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.396424004 + -1.5 x = -1.396424004 + -1.5 Combine like terms: -1.396424004 + -1.5 = -2.896424004 x = -2.896424004 Simplifying x = -2.896424004Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.103575996, -2.896424004}
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