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Simplifying 3.14x2 + 3.14x + -5 = 0 Reorder the terms: -5 + 3.14x + 3.14x2 = 0 Solving -5 + 3.14x + 3.14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.14 the coefficient of the squared term: Divide each side by '3.14'. -1.592356688 + x + x2 = 0 Move the constant term to the right: Add '1.592356688' to each side of the equation. -1.592356688 + x + 1.592356688 + x2 = 0 + 1.592356688 Reorder the terms: -1.592356688 + 1.592356688 + x + x2 = 0 + 1.592356688 Combine like terms: -1.592356688 + 1.592356688 = 0.000000000 0.000000000 + x + x2 = 0 + 1.592356688 x + x2 = 0 + 1.592356688 Combine like terms: 0 + 1.592356688 = 1.592356688 x + x2 = 1.592356688 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. + 0.25 + x2 = 1.592356688 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.592356688 + 0.25 Combine like terms: 1.592356688 + 0.25 = 1.842356688 1.25 + x2 = 1.842356688 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.842356688 Calculate the square root of the right side: 1.357334405 Break this problem into two subproblems by setting (x + 0.5) equal to 1.357334405 and -1.357334405.Subproblem 1
x + 0.5 = 1.357334405 Simplifying x + 0.5 = 1.357334405 Reorder the terms: 0.5 + x = 1.357334405 Solving 0.5 + x = 1.357334405 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 = 1.357334405 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.357334405 + -0.5 x = 1.357334405 + -0.5 Combine like terms: 1.357334405 + -0.5 = 0.857334405 x = 0.857334405 Simplifying x = 0.857334405Subproblem 2
x + 0.5 = -1.357334405 Simplifying x + 0.5 = -1.357334405 Reorder the terms: 0.5 + x = -1.357334405 Solving 0.5 + x = -1.357334405 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 = -1.357334405 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.357334405 + -0.5 x = -1.357334405 + -0.5 Combine like terms: -1.357334405 + -0.5 = -1.857334405 x = -1.857334405 Simplifying x = -1.857334405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.857334405, -1.857334405}
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