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Simplifying (x + -8) + x2 + (x + -3) = 25 Reorder the terms: (-8 + x) + x2 + (x + -3) = 25 Remove parenthesis around (-8 + x) -8 + x + x2 + (x + -3) = 25 Reorder the terms: -8 + x + x2 + (-3 + x) = 25 Remove parenthesis around (-3 + x) -8 + x + x2 + -3 + x = 25 Reorder the terms: -8 + -3 + x + x + x2 = 25 Combine like terms: -8 + -3 = -11 -11 + x + x + x2 = 25 Combine like terms: x + x = 2x -11 + 2x + x2 = 25 Solving -11 + 2x + x2 = 25 Solving for variable 'x'. Reorder the terms: -11 + -25 + 2x + x2 = 25 + -25 Combine like terms: -11 + -25 = -36 -36 + 2x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -36 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 2x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 2x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 2x + x2 = 0 + 36 2x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 2x + x2 = 36 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 36 + 1 Reorder the terms: 1 + 2x + x2 = 36 + 1 Combine like terms: 36 + 1 = 37 1 + 2x + x2 = 37 Factor a perfect square on the left side: (x + 1)(x + 1) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 1) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 1 = 6.08276253 Simplifying x + 1 = 6.08276253 Reorder the terms: 1 + x = 6.08276253 Solving 1 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.08276253 + -1 x = 6.08276253 + -1 Combine like terms: 6.08276253 + -1 = 5.08276253 x = 5.08276253 Simplifying x = 5.08276253Subproblem 2
x + 1 = -6.08276253 Simplifying x + 1 = -6.08276253 Reorder the terms: 1 + x = -6.08276253 Solving 1 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.08276253 + -1 x = -6.08276253 + -1 Combine like terms: -6.08276253 + -1 = -7.08276253 x = -7.08276253 Simplifying x = -7.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.08276253, -7.08276253}
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