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Simplifying x2 + 32x + -22 = 0 Reorder the terms: -22 + 32x + x2 = 0 Solving -22 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 32x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 32x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 32x + x2 = 0 + 22 32x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 32x + x2 = 22 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 = 22 + 256 Reorder the terms: 256 + 32x + x2 = 22 + 256 Combine like terms: 22 + 256 = 278 256 + 32x + x2 = 278 Factor a perfect square on the left side: (x + 16)(x + 16) = 278 Calculate the square root of the right side: 16.673332001 Break this problem into two subproblems by setting (x + 16) equal to 16.673332001 and -16.673332001.Subproblem 1
x + 16 = 16.673332001 Simplifying x + 16 = 16.673332001 Reorder the terms: 16 + x = 16.673332001 Solving 16 + x = 16.673332001 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 = 16.673332001 + -16 Combine like terms: 16 + -16 = 0 0 + x = 16.673332001 + -16 x = 16.673332001 + -16 Combine like terms: 16.673332001 + -16 = 0.673332001 x = 0.673332001 Simplifying x = 0.673332001Subproblem 2
x + 16 = -16.673332001 Simplifying x + 16 = -16.673332001 Reorder the terms: 16 + x = -16.673332001 Solving 16 + x = -16.673332001 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 = -16.673332001 + -16 Combine like terms: 16 + -16 = 0 0 + x = -16.673332001 + -16 x = -16.673332001 + -16 Combine like terms: -16.673332001 + -16 = -32.673332001 x = -32.673332001 Simplifying x = -32.673332001Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.673332001, -32.673332001}
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