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Simplifying 7x2 + 53x + 8 = 0 Reorder the terms: 8 + 53x + 7x2 = 0 Solving 8 + 53x + 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'. 1.142857143 + 7.571428571x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + 7.571428571x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + 7.571428571x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + 7.571428571x + x2 = 0 + -1.142857143 7.571428571x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 7.571428571x + x2 = -1.142857143 The x term is 7.571428571x. Take half its coefficient (3.785714286). Square it (14.33163266) and add it to both sides. Add '14.33163266' to each side of the equation. 7.571428571x + 14.33163266 + x2 = -1.142857143 + 14.33163266 Reorder the terms: 14.33163266 + 7.571428571x + x2 = -1.142857143 + 14.33163266 Combine like terms: -1.142857143 + 14.33163266 = 13.188775517 14.33163266 + 7.571428571x + x2 = 13.188775517 Factor a perfect square on the left side: (x + 3.785714286)(x + 3.785714286) = 13.188775517 Calculate the square root of the right side: 3.631635378 Break this problem into two subproblems by setting (x + 3.785714286) equal to 3.631635378 and -3.631635378.Subproblem 1
x + 3.785714286 = 3.631635378 Simplifying x + 3.785714286 = 3.631635378 Reorder the terms: 3.785714286 + x = 3.631635378 Solving 3.785714286 + x = 3.631635378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.785714286' to each side of the equation. 3.785714286 + -3.785714286 + x = 3.631635378 + -3.785714286 Combine like terms: 3.785714286 + -3.785714286 = 0.000000000 0.000000000 + x = 3.631635378 + -3.785714286 x = 3.631635378 + -3.785714286 Combine like terms: 3.631635378 + -3.785714286 = -0.154078908 x = -0.154078908 Simplifying x = -0.154078908Subproblem 2
x + 3.785714286 = -3.631635378 Simplifying x + 3.785714286 = -3.631635378 Reorder the terms: 3.785714286 + x = -3.631635378 Solving 3.785714286 + x = -3.631635378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.785714286' to each side of the equation. 3.785714286 + -3.785714286 + x = -3.631635378 + -3.785714286 Combine like terms: 3.785714286 + -3.785714286 = 0.000000000 0.000000000 + x = -3.631635378 + -3.785714286 x = -3.631635378 + -3.785714286 Combine like terms: -3.631635378 + -3.785714286 = -7.417349664 x = -7.417349664 Simplifying x = -7.417349664Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.154078908, -7.417349664}
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