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Simplifying 7x2 + 48x + 64 = 0 Reorder the terms: 64 + 48x + 7x2 = 0 Solving 64 + 48x + 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'. 9.142857143 + 6.857142857x + x2 = 0 Move the constant term to the right: Add '-9.142857143' to each side of the equation. 9.142857143 + 6.857142857x + -9.142857143 + x2 = 0 + -9.142857143 Reorder the terms: 9.142857143 + -9.142857143 + 6.857142857x + x2 = 0 + -9.142857143 Combine like terms: 9.142857143 + -9.142857143 = 0.000000000 0.000000000 + 6.857142857x + x2 = 0 + -9.142857143 6.857142857x + x2 = 0 + -9.142857143 Combine like terms: 0 + -9.142857143 = -9.142857143 6.857142857x + x2 = -9.142857143 The x term is 6.857142857x. Take half its coefficient (3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. 6.857142857x + 11.75510204 + x2 = -9.142857143 + 11.75510204 Reorder the terms: 11.75510204 + 6.857142857x + x2 = -9.142857143 + 11.75510204 Combine like terms: -9.142857143 + 11.75510204 = 2.612244897 11.75510204 + 6.857142857x + x2 = 2.612244897 Factor a perfect square on the left side: (x + 3.428571429)(x + 3.428571429) = 2.612244897 Calculate the square root of the right side: 1.616244071 Break this problem into two subproblems by setting (x + 3.428571429) equal to 1.616244071 and -1.616244071.Subproblem 1
x + 3.428571429 = 1.616244071 Simplifying x + 3.428571429 = 1.616244071 Reorder the terms: 3.428571429 + x = 1.616244071 Solving 3.428571429 + x = 1.616244071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + x = 1.616244071 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + x = 1.616244071 + -3.428571429 x = 1.616244071 + -3.428571429 Combine like terms: 1.616244071 + -3.428571429 = -1.812327358 x = -1.812327358 Simplifying x = -1.812327358Subproblem 2
x + 3.428571429 = -1.616244071 Simplifying x + 3.428571429 = -1.616244071 Reorder the terms: 3.428571429 + x = -1.616244071 Solving 3.428571429 + x = -1.616244071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + x = -1.616244071 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + x = -1.616244071 + -3.428571429 x = -1.616244071 + -3.428571429 Combine like terms: -1.616244071 + -3.428571429 = -5.0448155 x = -5.0448155 Simplifying x = -5.0448155Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.812327358, -5.0448155}
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