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Simplifying x2 + 8x + -731 = 0 Reorder the terms: -731 + 8x + x2 = 0 Solving -731 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '731' to each side of the equation. -731 + 8x + 731 + x2 = 0 + 731 Reorder the terms: -731 + 731 + 8x + x2 = 0 + 731 Combine like terms: -731 + 731 = 0 0 + 8x + x2 = 0 + 731 8x + x2 = 0 + 731 Combine like terms: 0 + 731 = 731 8x + x2 = 731 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 731 + 16 Reorder the terms: 16 + 8x + x2 = 731 + 16 Combine like terms: 731 + 16 = 747 16 + 8x + x2 = 747 Factor a perfect square on the left side: (x + 4)(x + 4) = 747 Calculate the square root of the right side: 27.331300737 Break this problem into two subproblems by setting (x + 4) equal to 27.331300737 and -27.331300737.Subproblem 1
x + 4 = 27.331300737 Simplifying x + 4 = 27.331300737 Reorder the terms: 4 + x = 27.331300737 Solving 4 + x = 27.331300737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 27.331300737 + -4 Combine like terms: 4 + -4 = 0 0 + x = 27.331300737 + -4 x = 27.331300737 + -4 Combine like terms: 27.331300737 + -4 = 23.331300737 x = 23.331300737 Simplifying x = 23.331300737Subproblem 2
x + 4 = -27.331300737 Simplifying x + 4 = -27.331300737 Reorder the terms: 4 + x = -27.331300737 Solving 4 + x = -27.331300737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -27.331300737 + -4 Combine like terms: 4 + -4 = 0 0 + x = -27.331300737 + -4 x = -27.331300737 + -4 Combine like terms: -27.331300737 + -4 = -31.331300737 x = -31.331300737 Simplifying x = -31.331300737Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.331300737, -31.331300737}
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