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Simplifying 4x2 + x + -0.1 = 0 Reorder the terms: -0.1 + x + 4x2 = 0 Solving -0.1 + x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.025 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.025' to each side of the equation. -0.025 + 0.25x + 0.025 + x2 = 0 + 0.025 Reorder the terms: -0.025 + 0.025 + 0.25x + x2 = 0 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + 0.25x + x2 = 0 + 0.025 0.25x + x2 = 0 + 0.025 Combine like terms: 0 + 0.025 = 0.025 0.25x + x2 = 0.025 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = 0.025 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 0.025 + 0.25 Combine like terms: 0.025 + 0.25 = 0.275 0.25 + 0.25x + x2 = 0.275 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.275 Calculate the square root of the right side: 0.524404424 Break this problem into two subproblems by setting (x + 0.5) equal to 0.524404424 and -0.524404424.Subproblem 1
x + 0.5 = 0.524404424 Simplifying x + 0.5 = 0.524404424 Reorder the terms: 0.5 + x = 0.524404424 Solving 0.5 + x = 0.524404424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.524404424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.524404424 + -0.5 x = 0.524404424 + -0.5 Combine like terms: 0.524404424 + -0.5 = 0.024404424 x = 0.024404424 Simplifying x = 0.024404424Subproblem 2
x + 0.5 = -0.524404424 Simplifying x + 0.5 = -0.524404424 Reorder the terms: 0.5 + x = -0.524404424 Solving 0.5 + x = -0.524404424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.524404424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.524404424 + -0.5 x = -0.524404424 + -0.5 Combine like terms: -0.524404424 + -0.5 = -1.024404424 x = -1.024404424 Simplifying x = -1.024404424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.024404424, -1.024404424}
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