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Simplifying 5x2 + 2x + -0.5 = 0 Reorder the terms: -0.5 + 2x + 5x2 = 0 Solving -0.5 + 2x + 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'. -0.1 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.4x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.4x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.4x + x2 = 0 + 0.1 0.4x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.4x + x2 = 0.1 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.1 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.1 + 0.04 Combine like terms: 0.1 + 0.04 = 0.14 0.04 + 0.4x + x2 = 0.14 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.14 Calculate the square root of the right side: 0.374165739 Break this problem into two subproblems by setting (x + 0.2) equal to 0.374165739 and -0.374165739.Subproblem 1
x + 0.2 = 0.374165739 Simplifying x + 0.2 = 0.374165739 Reorder the terms: 0.2 + x = 0.374165739 Solving 0.2 + x = 0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.374165739 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.374165739 + -0.2 x = 0.374165739 + -0.2 Combine like terms: 0.374165739 + -0.2 = 0.174165739 x = 0.174165739 Simplifying x = 0.174165739Subproblem 2
x + 0.2 = -0.374165739 Simplifying x + 0.2 = -0.374165739 Reorder the terms: 0.2 + x = -0.374165739 Solving 0.2 + x = -0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.374165739 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.374165739 + -0.2 x = -0.374165739 + -0.2 Combine like terms: -0.374165739 + -0.2 = -0.574165739 x = -0.574165739 Simplifying x = -0.574165739Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.174165739, -0.574165739}
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