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Simplifying 13 + -2x = x2 + -25 Reorder the terms: 13 + -2x = -25 + x2 Solving 13 + -2x = -25 + x2 Solving for variable 'x'. Reorder the terms: 13 + 25 + -2x + -1x2 = -25 + x2 + 25 + -1x2 Combine like terms: 13 + 25 = 38 38 + -2x + -1x2 = -25 + x2 + 25 + -1x2 Reorder the terms: 38 + -2x + -1x2 = -25 + 25 + x2 + -1x2 Combine like terms: -25 + 25 = 0 38 + -2x + -1x2 = 0 + x2 + -1x2 38 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 38 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -38 + 2x + x2 = 0 Move the constant term to the right: Add '38' to each side of the equation. -38 + 2x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 2x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 2x + x2 = 0 + 38 2x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 2x + x2 = 38 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 = 38 + 1 Reorder the terms: 1 + 2x + x2 = 38 + 1 Combine like terms: 38 + 1 = 39 1 + 2x + x2 = 39 Factor a perfect square on the left side: (x + 1)(x + 1) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 1) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 1 = 6.244997998 Simplifying x + 1 = 6.244997998 Reorder the terms: 1 + x = 6.244997998 Solving 1 + x = 6.244997998 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 = 6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.244997998 + -1 x = 6.244997998 + -1 Combine like terms: 6.244997998 + -1 = 5.244997998 x = 5.244997998 Simplifying x = 5.244997998Subproblem 2
x + 1 = -6.244997998 Simplifying x + 1 = -6.244997998 Reorder the terms: 1 + x = -6.244997998 Solving 1 + x = -6.244997998 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 = -6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.244997998 + -1 x = -6.244997998 + -1 Combine like terms: -6.244997998 + -1 = -7.244997998 x = -7.244997998 Simplifying x = -7.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.244997998, -7.244997998}
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