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Simplifying x2 + 32x + 256 = 33 Reorder the terms: 256 + 32x + x2 = 33 Solving 256 + 32x + x2 = 33 Solving for variable 'x'. Reorder the terms: 256 + -33 + 32x + x2 = 33 + -33 Combine like terms: 256 + -33 = 223 223 + 32x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 223 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-223' to each side of the equation. 223 + 32x + -223 + x2 = 0 + -223 Reorder the terms: 223 + -223 + 32x + x2 = 0 + -223 Combine like terms: 223 + -223 = 0 0 + 32x + x2 = 0 + -223 32x + x2 = 0 + -223 Combine like terms: 0 + -223 = -223 32x + x2 = -223 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 = -223 + 256 Reorder the terms: 256 + 32x + x2 = -223 + 256 Combine like terms: -223 + 256 = 33 256 + 32x + x2 = 33 Factor a perfect square on the left side: (x + 16)(x + 16) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 16) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 16 = 5.744562647 Simplifying x + 16 = 5.744562647 Reorder the terms: 16 + x = 5.744562647 Solving 16 + x = 5.744562647 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 = 5.744562647 + -16 Combine like terms: 16 + -16 = 0 0 + x = 5.744562647 + -16 x = 5.744562647 + -16 Combine like terms: 5.744562647 + -16 = -10.255437353 x = -10.255437353 Simplifying x = -10.255437353Subproblem 2
x + 16 = -5.744562647 Simplifying x + 16 = -5.744562647 Reorder the terms: 16 + x = -5.744562647 Solving 16 + x = -5.744562647 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 = -5.744562647 + -16 Combine like terms: 16 + -16 = 0 0 + x = -5.744562647 + -16 x = -5.744562647 + -16 Combine like terms: -5.744562647 + -16 = -21.744562647 x = -21.744562647 Simplifying x = -21.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.255437353, -21.744562647}
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