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Simplifying 19 = 7x2 + -5x Reorder the terms: 19 = -5x + 7x2 Solving 19 = -5x + 7x2 Solving for variable 'x'. Reorder the terms: 19 + 5x + -7x2 = -5x + 5x + 7x2 + -7x2 Combine like terms: -5x + 5x = 0 19 + 5x + -7x2 = 0 + 7x2 + -7x2 19 + 5x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 19 + 5x + -7x2 = 0 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 = 2.0429176742 x = 2.0429176742 Simplifying x = 2.0429176742Subproblem 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 = -1.3286319598 x = -1.3286319598 Simplifying x = -1.3286319598Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0429176742, -1.3286319598}
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