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Simplifying 7x2 + 5x + -19 = 0 Reorder the terms: -19 + 5x + 7x2 = 0 Solving -19 + 5x + 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'. -2.714285714 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + 0.7142857143x + 2.714285714 + x2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + 0.7142857143x + x2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + 0.7142857143x + x2 = 0 + 2.714285714 0.7142857143x + x2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 0.7142857143x + x2 = 2.714285714 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 2.714285714 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 2.714285714 + 0.1275510204 Combine like terms: 2.714285714 + 0.1275510204 = 2.8418367344 0.1275510204 + 0.7142857143x + x2 = 2.8418367344 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 2.8418367344 Calculate the square root of the right side: 1.685774817 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 1.685774817 and -1.685774817.Subproblem 1
x + 0.3571428572 = 1.685774817 Simplifying x + 0.3571428572 = 1.685774817 Reorder the terms: 0.3571428572 + x = 1.685774817 Solving 0.3571428572 + x = 1.685774817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 1.685774817 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 1.685774817 + -0.3571428572 x = 1.685774817 + -0.3571428572 Combine like terms: 1.685774817 + -0.3571428572 = 1.3286319598 x = 1.3286319598 Simplifying x = 1.3286319598Subproblem 2
x + 0.3571428572 = -1.685774817 Simplifying x + 0.3571428572 = -1.685774817 Reorder the terms: 0.3571428572 + x = -1.685774817 Solving 0.3571428572 + x = -1.685774817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -1.685774817 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -1.685774817 + -0.3571428572 x = -1.685774817 + -0.3571428572 Combine like terms: -1.685774817 + -0.3571428572 = -2.0429176742 x = -2.0429176742 Simplifying x = -2.0429176742Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3286319598, -2.0429176742}
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