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Simplifying 8x2 + 52x + 7 = 0 Reorder the terms: 7 + 52x + 8x2 = 0 Solving 7 + 52x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + 6.5x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + 6.5x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + 6.5x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + 6.5x + x2 = 0 + -0.875 6.5x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 6.5x + x2 = -0.875 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -0.875 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -0.875 + 10.5625 Combine like terms: -0.875 + 10.5625 = 9.6875 10.5625 + 6.5x + x2 = 9.6875 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 9.6875 Calculate the square root of the right side: 3.112474899 Break this problem into two subproblems by setting (x + 3.25) equal to 3.112474899 and -3.112474899.Subproblem 1
x + 3.25 = 3.112474899 Simplifying x + 3.25 = 3.112474899 Reorder the terms: 3.25 + x = 3.112474899 Solving 3.25 + x = 3.112474899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.112474899 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.112474899 + -3.25 x = 3.112474899 + -3.25 Combine like terms: 3.112474899 + -3.25 = -0.137525101 x = -0.137525101 Simplifying x = -0.137525101Subproblem 2
x + 3.25 = -3.112474899 Simplifying x + 3.25 = -3.112474899 Reorder the terms: 3.25 + x = -3.112474899 Solving 3.25 + x = -3.112474899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.112474899 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.112474899 + -3.25 x = -3.112474899 + -3.25 Combine like terms: -3.112474899 + -3.25 = -6.362474899 x = -6.362474899 Simplifying x = -6.362474899Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.137525101, -6.362474899}
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