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Simplifying x + 14x2 + -240 = 0 Reorder the terms: -240 + x + 14x2 = 0 Solving -240 + 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'. -17.14285714 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '17.14285714' to each side of the equation. -17.14285714 + 0.07142857143x + 17.14285714 + x2 = 0 + 17.14285714 Reorder the terms: -17.14285714 + 17.14285714 + 0.07142857143x + x2 = 0 + 17.14285714 Combine like terms: -17.14285714 + 17.14285714 = 0.00000000 0.00000000 + 0.07142857143x + x2 = 0 + 17.14285714 0.07142857143x + x2 = 0 + 17.14285714 Combine like terms: 0 + 17.14285714 = 17.14285714 0.07142857143x + x2 = 17.14285714 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 = 17.14285714 + 0.25 Reorder the terms: 0.25 + 0.07142857143x + x2 = 17.14285714 + 0.25 Combine like terms: 17.14285714 + 0.25 = 17.39285714 0.25 + 0.07142857143x + x2 = 17.39285714 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 17.39285714 Calculate the square root of the right side: 4.17047445 Break this problem into two subproblems by setting (x + 0.5) equal to 4.17047445 and -4.17047445.Subproblem 1
x + 0.5 = 4.17047445 Simplifying x + 0.5 = 4.17047445 Reorder the terms: 0.5 + x = 4.17047445 Solving 0.5 + x = 4.17047445 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 = 4.17047445 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.17047445 + -0.5 x = 4.17047445 + -0.5 Combine like terms: 4.17047445 + -0.5 = 3.67047445 x = 3.67047445 Simplifying x = 3.67047445Subproblem 2
x + 0.5 = -4.17047445 Simplifying x + 0.5 = -4.17047445 Reorder the terms: 0.5 + x = -4.17047445 Solving 0.5 + x = -4.17047445 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 = -4.17047445 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.17047445 + -0.5 x = -4.17047445 + -0.5 Combine like terms: -4.17047445 + -0.5 = -4.67047445 x = -4.67047445 Simplifying x = -4.67047445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.67047445, -4.67047445}
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