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Simplifying x2 = 25 + -2x Solving x2 = 25 + -2x Solving for variable 'x'. Reorder the terms: -25 + 2x + x2 = 25 + -2x + -25 + 2x Reorder the terms: -25 + 2x + x2 = 25 + -25 + -2x + 2x Combine like terms: 25 + -25 = 0 -25 + 2x + x2 = 0 + -2x + 2x -25 + 2x + x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -25 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 2x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2x + x2 = 0 + 25 2x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 2x + x2 = 25 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 = 25 + 1 Reorder the terms: 1 + 2x + x2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2x + x2 = 26 Factor a perfect square on the left side: (x + 1)(x + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 1 = 5.099019514 Simplifying x + 1 = 5.099019514 Reorder the terms: 1 + x = 5.099019514 Solving 1 + x = 5.099019514 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 = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.099019514 + -1 x = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 x = 4.099019514 Simplifying x = 4.099019514Subproblem 2
x + 1 = -5.099019514 Simplifying x + 1 = -5.099019514 Reorder the terms: 1 + x = -5.099019514 Solving 1 + x = -5.099019514 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 = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.099019514 + -1 x = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 x = -6.099019514 Simplifying x = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.099019514, -6.099019514}
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