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Simplifying x2 + 16x + -75 = 0 Reorder the terms: -75 + 16x + x2 = 0 Solving -75 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 16x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 16x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 16x + x2 = 0 + 75 16x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 16x + x2 = 75 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 75 + 64 Reorder the terms: 64 + 16x + x2 = 75 + 64 Combine like terms: 75 + 64 = 139 64 + 16x + x2 = 139 Factor a perfect square on the left side: (x + 8)(x + 8) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (x + 8) equal to 11.789826123 and -11.789826123.Subproblem 1
x + 8 = 11.789826123 Simplifying x + 8 = 11.789826123 Reorder the terms: 8 + x = 11.789826123 Solving 8 + x = 11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 11.789826123 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.789826123 + -8 x = 11.789826123 + -8 Combine like terms: 11.789826123 + -8 = 3.789826123 x = 3.789826123 Simplifying x = 3.789826123Subproblem 2
x + 8 = -11.789826123 Simplifying x + 8 = -11.789826123 Reorder the terms: 8 + x = -11.789826123 Solving 8 + x = -11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -11.789826123 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.789826123 + -8 x = -11.789826123 + -8 Combine like terms: -11.789826123 + -8 = -19.789826123 x = -19.789826123 Simplifying x = -19.789826123Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.789826123, -19.789826123}
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