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Simplifying x2 + 10x = 238 Reorder the terms: 10x + x2 = 238 Solving 10x + x2 = 238 Solving for variable 'x'. Reorder the terms: -238 + 10x + x2 = 238 + -238 Combine like terms: 238 + -238 = 0 -238 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '238' to each side of the equation. -238 + 10x + 238 + x2 = 0 + 238 Reorder the terms: -238 + 238 + 10x + x2 = 0 + 238 Combine like terms: -238 + 238 = 0 0 + 10x + x2 = 0 + 238 10x + x2 = 0 + 238 Combine like terms: 0 + 238 = 238 10x + x2 = 238 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 238 + 25 Reorder the terms: 25 + 10x + x2 = 238 + 25 Combine like terms: 238 + 25 = 263 25 + 10x + x2 = 263 Factor a perfect square on the left side: (x + 5)(x + 5) = 263 Calculate the square root of the right side: 16.21727474 Break this problem into two subproblems by setting (x + 5) equal to 16.21727474 and -16.21727474.Subproblem 1
x + 5 = 16.21727474 Simplifying x + 5 = 16.21727474 Reorder the terms: 5 + x = 16.21727474 Solving 5 + x = 16.21727474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 16.21727474 + -5 Combine like terms: 5 + -5 = 0 0 + x = 16.21727474 + -5 x = 16.21727474 + -5 Combine like terms: 16.21727474 + -5 = 11.21727474 x = 11.21727474 Simplifying x = 11.21727474Subproblem 2
x + 5 = -16.21727474 Simplifying x + 5 = -16.21727474 Reorder the terms: 5 + x = -16.21727474 Solving 5 + x = -16.21727474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -16.21727474 + -5 Combine like terms: 5 + -5 = 0 0 + x = -16.21727474 + -5 x = -16.21727474 + -5 Combine like terms: -16.21727474 + -5 = -21.21727474 x = -21.21727474 Simplifying x = -21.21727474Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.21727474, -21.21727474}
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