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Simplifying x2 + 10x + 25 = 22 Reorder the terms: 25 + 10x + x2 = 22 Solving 25 + 10x + x2 = 22 Solving for variable 'x'. Reorder the terms: 25 + -22 + 10x + x2 = 22 + -22 Combine like terms: 25 + -22 = 3 3 + 10x + x2 = 22 + -22 Combine like terms: 22 + -22 = 0 3 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 10x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 10x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 10x + x2 = 0 + -3 10x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 10x + x2 = -3 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 = -3 + 25 Reorder the terms: 25 + 10x + x2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + 10x + x2 = 22 Factor a perfect square on the left side: (x + 5)(x + 5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 5) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 5 = 4.69041576 Simplifying x + 5 = 4.69041576 Reorder the terms: 5 + x = 4.69041576 Solving 5 + x = 4.69041576 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 = 4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.69041576 + -5 x = 4.69041576 + -5 Combine like terms: 4.69041576 + -5 = -0.30958424 x = -0.30958424 Simplifying x = -0.30958424Subproblem 2
x + 5 = -4.69041576 Simplifying x + 5 = -4.69041576 Reorder the terms: 5 + x = -4.69041576 Solving 5 + x = -4.69041576 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 = -4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.69041576 + -5 x = -4.69041576 + -5 Combine like terms: -4.69041576 + -5 = -9.69041576 x = -9.69041576 Simplifying x = -9.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.30958424, -9.69041576}
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