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Simplifying 7x2 + 16x + -40 = 0 Reorder the terms: -40 + 16x + 7x2 = 0 Solving -40 + 16x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.714285714 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + 2.285714286x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + 2.285714286x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + 2.285714286x + x2 = 0 + 5.714285714 2.285714286x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 2.285714286x + x2 = 5.714285714 The x term is 2.285714286x. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286x + 1.306122449 + x2 = 5.714285714 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = 5.714285714 + 1.306122449 Combine like terms: 5.714285714 + 1.306122449 = 7.020408163 1.306122449 + 2.285714286x + x2 = 7.020408163 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 7.020408163 Calculate the square root of the right side: 2.649605284 Break this problem into two subproblems by setting (x + 1.142857143) equal to 2.649605284 and -2.649605284.Subproblem 1
x + 1.142857143 = 2.649605284 Simplifying x + 1.142857143 = 2.649605284 Reorder the terms: 1.142857143 + x = 2.649605284 Solving 1.142857143 + x = 2.649605284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = 2.649605284 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 2.649605284 + -1.142857143 x = 2.649605284 + -1.142857143 Combine like terms: 2.649605284 + -1.142857143 = 1.506748141 x = 1.506748141 Simplifying x = 1.506748141Subproblem 2
x + 1.142857143 = -2.649605284 Simplifying x + 1.142857143 = -2.649605284 Reorder the terms: 1.142857143 + x = -2.649605284 Solving 1.142857143 + x = -2.649605284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = -2.649605284 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -2.649605284 + -1.142857143 x = -2.649605284 + -1.142857143 Combine like terms: -2.649605284 + -1.142857143 = -3.792462427 x = -3.792462427 Simplifying x = -3.792462427Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.506748141, -3.792462427}
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