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Simplifying 14x2 + x + -5 = 0 Reorder the terms: -5 + x + 14x2 = 0 Solving -5 + x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.3571428571 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + 0.07142857143x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + 0.07142857143x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + 0.07142857143x + x2 = 0 + 0.3571428571 0.07142857143x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 0.07142857143x + x2 = 0.3571428571 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. 0.07142857143x + 0.25 + x2 = 0.3571428571 + 0.25 Reorder the terms: 0.25 + 0.07142857143x + x2 = 0.3571428571 + 0.25 Combine like terms: 0.3571428571 + 0.25 = 0.6071428571 0.25 + 0.07142857143x + x2 = 0.6071428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.6071428571 Calculate the square root of the right side: 0.779193722 Break this problem into two subproblems by setting (x + 0.5) equal to 0.779193722 and -0.779193722.Subproblem 1
x + 0.5 = 0.779193722 Simplifying x + 0.5 = 0.779193722 Reorder the terms: 0.5 + x = 0.779193722 Solving 0.5 + x = 0.779193722 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 = 0.779193722 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.779193722 + -0.5 x = 0.779193722 + -0.5 Combine like terms: 0.779193722 + -0.5 = 0.279193722 x = 0.279193722 Simplifying x = 0.279193722Subproblem 2
x + 0.5 = -0.779193722 Simplifying x + 0.5 = -0.779193722 Reorder the terms: 0.5 + x = -0.779193722 Solving 0.5 + x = -0.779193722 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 = -0.779193722 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.779193722 + -0.5 x = -0.779193722 + -0.5 Combine like terms: -0.779193722 + -0.5 = -1.279193722 x = -1.279193722 Simplifying x = -1.279193722Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.279193722, -1.279193722}
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