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Simplifying x2 + 10x + 13 = 68 Reorder the terms: 13 + 10x + x2 = 68 Solving 13 + 10x + x2 = 68 Solving for variable 'x'. Reorder the terms: 13 + -68 + 10x + x2 = 68 + -68 Combine like terms: 13 + -68 = -55 -55 + 10x + x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -55 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 10x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 10x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 10x + x2 = 0 + 55 10x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 10x + x2 = 55 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 = 55 + 25 Reorder the terms: 25 + 10x + x2 = 55 + 25 Combine like terms: 55 + 25 = 80 25 + 10x + x2 = 80 Factor a perfect square on the left side: (x + 5)(x + 5) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + 5) equal to 8.94427191 and -8.94427191.Subproblem 1
x + 5 = 8.94427191 Simplifying x + 5 = 8.94427191 Reorder the terms: 5 + x = 8.94427191 Solving 5 + x = 8.94427191 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 = 8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.94427191 + -5 x = 8.94427191 + -5 Combine like terms: 8.94427191 + -5 = 3.94427191 x = 3.94427191 Simplifying x = 3.94427191Subproblem 2
x + 5 = -8.94427191 Simplifying x + 5 = -8.94427191 Reorder the terms: 5 + x = -8.94427191 Solving 5 + x = -8.94427191 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 = -8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.94427191 + -5 x = -8.94427191 + -5 Combine like terms: -8.94427191 + -5 = -13.94427191 x = -13.94427191 Simplifying x = -13.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.94427191, -13.94427191}
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