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Simplifying x2 + 58x + -448 = 0 Reorder the terms: -448 + 58x + x2 = 0 Solving -448 + 58x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '448' to each side of the equation. -448 + 58x + 448 + x2 = 0 + 448 Reorder the terms: -448 + 448 + 58x + x2 = 0 + 448 Combine like terms: -448 + 448 = 0 0 + 58x + x2 = 0 + 448 58x + x2 = 0 + 448 Combine like terms: 0 + 448 = 448 58x + x2 = 448 The x term is 58x. Take half its coefficient (29). Square it (841) and add it to both sides. Add '841' to each side of the equation. 58x + 841 + x2 = 448 + 841 Reorder the terms: 841 + 58x + x2 = 448 + 841 Combine like terms: 448 + 841 = 1289 841 + 58x + x2 = 1289 Factor a perfect square on the left side: (x + 29)(x + 29) = 1289 Calculate the square root of the right side: 35.902646142 Break this problem into two subproblems by setting (x + 29) equal to 35.902646142 and -35.902646142.Subproblem 1
x + 29 = 35.902646142 Simplifying x + 29 = 35.902646142 Reorder the terms: 29 + x = 35.902646142 Solving 29 + x = 35.902646142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = 35.902646142 + -29 Combine like terms: 29 + -29 = 0 0 + x = 35.902646142 + -29 x = 35.902646142 + -29 Combine like terms: 35.902646142 + -29 = 6.902646142 x = 6.902646142 Simplifying x = 6.902646142Subproblem 2
x + 29 = -35.902646142 Simplifying x + 29 = -35.902646142 Reorder the terms: 29 + x = -35.902646142 Solving 29 + x = -35.902646142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = -35.902646142 + -29 Combine like terms: 29 + -29 = 0 0 + x = -35.902646142 + -29 x = -35.902646142 + -29 Combine like terms: -35.902646142 + -29 = -64.902646142 x = -64.902646142 Simplifying x = -64.902646142Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.902646142, -64.902646142}
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