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Simplifying x2 + 1 = 5x + 2 + 50 Reorder the terms: 1 + x2 = 5x + 2 + 50 Reorder the terms: 1 + x2 = 2 + 50 + 5x Combine like terms: 2 + 50 = 52 1 + x2 = 52 + 5x Solving 1 + x2 = 52 + 5x Solving for variable 'x'. Reorder the terms: 1 + -52 + -5x + x2 = 52 + 5x + -52 + -5x Combine like terms: 1 + -52 = -51 -51 + -5x + x2 = 52 + 5x + -52 + -5x Reorder the terms: -51 + -5x + x2 = 52 + -52 + 5x + -5x Combine like terms: 52 + -52 = 0 -51 + -5x + x2 = 0 + 5x + -5x -51 + -5x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -51 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -5x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -5x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -5x + x2 = 0 + 51 -5x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -5x + x2 = 51 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 51 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 51 + 6.25 Combine like terms: 51 + 6.25 = 57.25 6.25 + -5x + x2 = 57.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + -2.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + -2.5 = 7.566372975 Simplifying x + -2.5 = 7.566372975 Reorder the terms: -2.5 + x = 7.566372975 Solving -2.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.566372975 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.566372975 + 2.5 x = 7.566372975 + 2.5 Combine like terms: 7.566372975 + 2.5 = 10.066372975 x = 10.066372975 Simplifying x = 10.066372975Subproblem 2
x + -2.5 = -7.566372975 Simplifying x + -2.5 = -7.566372975 Reorder the terms: -2.5 + x = -7.566372975 Solving -2.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.566372975 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.566372975 + 2.5 x = -7.566372975 + 2.5 Combine like terms: -7.566372975 + 2.5 = -5.066372975 x = -5.066372975 Simplifying x = -5.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.066372975, -5.066372975}
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