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Simplifying x2 + 8x = 25 Reorder the terms: 8x + x2 = 25 Solving 8x + x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 8x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 8x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 8x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 8x + x2 = 0 + 25 8x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 8x + x2 = 25 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 = 25 + 16 Reorder the terms: 16 + 8x + x2 = 25 + 16 Combine like terms: 25 + 16 = 41 16 + 8x + x2 = 41 Factor a perfect square on the left side: (x + 4)(x + 4) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 4) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 4 = 6.403124237 Simplifying x + 4 = 6.403124237 Reorder the terms: 4 + x = 6.403124237 Solving 4 + x = 6.403124237 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 = 6.403124237 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.403124237 + -4 x = 6.403124237 + -4 Combine like terms: 6.403124237 + -4 = 2.403124237 x = 2.403124237 Simplifying x = 2.403124237Subproblem 2
x + 4 = -6.403124237 Simplifying x + 4 = -6.403124237 Reorder the terms: 4 + x = -6.403124237 Solving 4 + x = -6.403124237 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 = -6.403124237 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.403124237 + -4 x = -6.403124237 + -4 Combine like terms: -6.403124237 + -4 = -10.403124237 x = -10.403124237 Simplifying x = -10.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.403124237, -10.403124237}
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