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Simplifying 5x2 + x + -2 = 0 Reorder the terms: -2 + x + 5x2 = 0 Solving -2 + x + 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'. -0.4 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.2x + x2 = 0 + 0.4 0.2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.2x + x2 = 0.4 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. 0.2x + 0.25 + x2 = 0.4 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 0.4 + 0.25 Combine like terms: 0.4 + 0.25 = 0.65 0.25 + 0.2x + x2 = 0.65 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (x + 0.5) equal to 0.806225775 and -0.806225775.Subproblem 1
x + 0.5 = 0.806225775 Simplifying x + 0.5 = 0.806225775 Reorder the terms: 0.5 + x = 0.806225775 Solving 0.5 + x = 0.806225775 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 = 0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.806225775 + -0.5 x = 0.806225775 + -0.5 Combine like terms: 0.806225775 + -0.5 = 0.306225775 x = 0.306225775 Simplifying x = 0.306225775Subproblem 2
x + 0.5 = -0.806225775 Simplifying x + 0.5 = -0.806225775 Reorder the terms: 0.5 + x = -0.806225775 Solving 0.5 + x = -0.806225775 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 = -0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.806225775 + -0.5 x = -0.806225775 + -0.5 Combine like terms: -0.806225775 + -0.5 = -1.306225775 x = -1.306225775 Simplifying x = -1.306225775Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.306225775, -1.306225775}
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