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Simplifying 7x2 + 5x + -56 = 0 Reorder the terms: -56 + 5x + 7x2 = 0 Solving -56 + 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'. -8 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 0.7142857143x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 0.7142857143x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 0.7142857143x + x2 = 0 + 8 0.7142857143x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 0.7142857143x + x2 = 8 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 = 8 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 8 + 0.1275510204 Combine like terms: 8 + 0.1275510204 = 8.1275510204 0.1275510204 + 0.7142857143x + x2 = 8.1275510204 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 8.1275510204 Calculate the square root of the right side: 2.850886006 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 2.850886006 and -2.850886006.Subproblem 1
x + 0.3571428572 = 2.850886006 Simplifying x + 0.3571428572 = 2.850886006 Reorder the terms: 0.3571428572 + x = 2.850886006 Solving 0.3571428572 + x = 2.850886006 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 = 2.850886006 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 2.850886006 + -0.3571428572 x = 2.850886006 + -0.3571428572 Combine like terms: 2.850886006 + -0.3571428572 = 2.4937431488 x = 2.4937431488 Simplifying x = 2.4937431488Subproblem 2
x + 0.3571428572 = -2.850886006 Simplifying x + 0.3571428572 = -2.850886006 Reorder the terms: 0.3571428572 + x = -2.850886006 Solving 0.3571428572 + x = -2.850886006 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 = -2.850886006 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -2.850886006 + -0.3571428572 x = -2.850886006 + -0.3571428572 Combine like terms: -2.850886006 + -0.3571428572 = -3.2080288632 x = -3.2080288632 Simplifying x = -3.2080288632Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4937431488, -3.2080288632}
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