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Simplifying x2 + 42 = 32x Reorder the terms: 42 + x2 = 32x Solving 42 + x2 = 32x Solving for variable 'x'. Reorder the terms: 42 + -32x + x2 = 32x + -32x Combine like terms: 32x + -32x = 0 42 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -32x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -32x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -32x + x2 = 0 + -42 -32x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -32x + x2 = -42 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -42 + 256 Reorder the terms: 256 + -32x + x2 = -42 + 256 Combine like terms: -42 + 256 = 214 256 + -32x + x2 = 214 Factor a perfect square on the left side: (x + -16)(x + -16) = 214 Calculate the square root of the right side: 14.628738838 Break this problem into two subproblems by setting (x + -16) equal to 14.628738838 and -14.628738838.Subproblem 1
x + -16 = 14.628738838 Simplifying x + -16 = 14.628738838 Reorder the terms: -16 + x = 14.628738838 Solving -16 + x = 14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 14.628738838 + 16 Combine like terms: -16 + 16 = 0 0 + x = 14.628738838 + 16 x = 14.628738838 + 16 Combine like terms: 14.628738838 + 16 = 30.628738838 x = 30.628738838 Simplifying x = 30.628738838Subproblem 2
x + -16 = -14.628738838 Simplifying x + -16 = -14.628738838 Reorder the terms: -16 + x = -14.628738838 Solving -16 + x = -14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -14.628738838 + 16 Combine like terms: -16 + 16 = 0 0 + x = -14.628738838 + 16 x = -14.628738838 + 16 Combine like terms: -14.628738838 + 16 = 1.371261162 x = 1.371261162 Simplifying x = 1.371261162Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.628738838, 1.371261162}
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