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Simplifying x2 + 10x + 10 = 25 Reorder the terms: 10 + 10x + x2 = 25 Solving 10 + 10x + x2 = 25 Solving for variable 'x'. Reorder the terms: 10 + -25 + 10x + x2 = 25 + -25 Combine like terms: 10 + -25 = -15 -15 + 10x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -15 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 10x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 10x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 10x + x2 = 0 + 15 10x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 10x + x2 = 15 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 = 15 + 25 Reorder the terms: 25 + 10x + x2 = 15 + 25 Combine like terms: 15 + 25 = 40 25 + 10x + x2 = 40 Factor a perfect square on the left side: (x + 5)(x + 5) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 5) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 5 = 6.32455532 Simplifying x + 5 = 6.32455532 Reorder the terms: 5 + x = 6.32455532 Solving 5 + x = 6.32455532 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 = 6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.32455532 + -5 x = 6.32455532 + -5 Combine like terms: 6.32455532 + -5 = 1.32455532 x = 1.32455532 Simplifying x = 1.32455532Subproblem 2
x + 5 = -6.32455532 Simplifying x + 5 = -6.32455532 Reorder the terms: 5 + x = -6.32455532 Solving 5 + x = -6.32455532 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 = -6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.32455532 + -5 x = -6.32455532 + -5 Combine like terms: -6.32455532 + -5 = -11.32455532 x = -11.32455532 Simplifying x = -11.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.32455532, -11.32455532}
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