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Simplifying 10x + 1 = 289 + -1x2 Reorder the terms: 1 + 10x = 289 + -1x2 Solving 1 + 10x = 289 + -1x2 Solving for variable 'x'. Reorder the terms: 1 + -289 + 10x + x2 = 289 + -1x2 + -289 + x2 Combine like terms: 1 + -289 = -288 -288 + 10x + x2 = 289 + -1x2 + -289 + x2 Reorder the terms: -288 + 10x + x2 = 289 + -289 + -1x2 + x2 Combine like terms: 289 + -289 = 0 -288 + 10x + x2 = 0 + -1x2 + x2 -288 + 10x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -288 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 10x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + 10x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 10x + x2 = 0 + 288 10x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 10x + x2 = 288 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 = 288 + 25 Reorder the terms: 25 + 10x + x2 = 288 + 25 Combine like terms: 288 + 25 = 313 25 + 10x + x2 = 313 Factor a perfect square on the left side: (x + 5)(x + 5) = 313 Calculate the square root of the right side: 17.691806013 Break this problem into two subproblems by setting (x + 5) equal to 17.691806013 and -17.691806013.Subproblem 1
x + 5 = 17.691806013 Simplifying x + 5 = 17.691806013 Reorder the terms: 5 + x = 17.691806013 Solving 5 + x = 17.691806013 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 = 17.691806013 + -5 Combine like terms: 5 + -5 = 0 0 + x = 17.691806013 + -5 x = 17.691806013 + -5 Combine like terms: 17.691806013 + -5 = 12.691806013 x = 12.691806013 Simplifying x = 12.691806013Subproblem 2
x + 5 = -17.691806013 Simplifying x + 5 = -17.691806013 Reorder the terms: 5 + x = -17.691806013 Solving 5 + x = -17.691806013 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 = -17.691806013 + -5 Combine like terms: 5 + -5 = 0 0 + x = -17.691806013 + -5 x = -17.691806013 + -5 Combine like terms: -17.691806013 + -5 = -22.691806013 x = -22.691806013 Simplifying x = -22.691806013Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.691806013, -22.691806013}
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