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Simplifying x2 + 42 = 16x Reorder the terms: 42 + x2 = 16x Solving 42 + x2 = 16x Solving for variable 'x'. Reorder the terms: 42 + -16x + x2 = 16x + -16x Combine like terms: 16x + -16x = 0 42 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -16x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -16x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -16x + x2 = 0 + -42 -16x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -16x + x2 = -42 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -42 + 64 Reorder the terms: 64 + -16x + x2 = -42 + 64 Combine like terms: -42 + 64 = 22 64 + -16x + x2 = 22 Factor a perfect square on the left side: (x + -8)(x + -8) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -8) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -8 = 4.69041576 Simplifying x + -8 = 4.69041576 Reorder the terms: -8 + x = 4.69041576 Solving -8 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 4.69041576 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4.69041576 + 8 x = 4.69041576 + 8 Combine like terms: 4.69041576 + 8 = 12.69041576 x = 12.69041576 Simplifying x = 12.69041576Subproblem 2
x + -8 = -4.69041576 Simplifying x + -8 = -4.69041576 Reorder the terms: -8 + x = -4.69041576 Solving -8 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -4.69041576 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4.69041576 + 8 x = -4.69041576 + 8 Combine like terms: -4.69041576 + 8 = 3.30958424 x = 3.30958424 Simplifying x = 3.30958424Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.69041576, 3.30958424}
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