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Simplifying (16 + x)(16 + x) = 1632 Multiply (16 + x) * (16 + x) (16(16 + x) + x(16 + x)) = 1632 ((16 * 16 + x * 16) + x(16 + x)) = 1632 ((256 + 16x) + x(16 + x)) = 1632 (256 + 16x + (16 * x + x * x)) = 1632 (256 + 16x + (16x + x2)) = 1632 Combine like terms: 16x + 16x = 32x (256 + 32x + x2) = 1632 Solving 256 + 32x + x2 = 1632 Solving for variable 'x'. Reorder the terms: 256 + -1632 + 32x + x2 = 1632 + -1632 Combine like terms: 256 + -1632 = -1376 -1376 + 32x + x2 = 1632 + -1632 Combine like terms: 1632 + -1632 = 0 -1376 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1376' to each side of the equation. -1376 + 32x + 1376 + x2 = 0 + 1376 Reorder the terms: -1376 + 1376 + 32x + x2 = 0 + 1376 Combine like terms: -1376 + 1376 = 0 0 + 32x + x2 = 0 + 1376 32x + x2 = 0 + 1376 Combine like terms: 0 + 1376 = 1376 32x + x2 = 1376 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 = 1376 + 256 Reorder the terms: 256 + 32x + x2 = 1376 + 256 Combine like terms: 1376 + 256 = 1632 256 + 32x + x2 = 1632 Factor a perfect square on the left side: (x + 16)(x + 16) = 1632 Calculate the square root of the right side: 40.398019753 Break this problem into two subproblems by setting (x + 16) equal to 40.398019753 and -40.398019753.Subproblem 1
x + 16 = 40.398019753 Simplifying x + 16 = 40.398019753 Reorder the terms: 16 + x = 40.398019753 Solving 16 + x = 40.398019753 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 = 40.398019753 + -16 Combine like terms: 16 + -16 = 0 0 + x = 40.398019753 + -16 x = 40.398019753 + -16 Combine like terms: 40.398019753 + -16 = 24.398019753 x = 24.398019753 Simplifying x = 24.398019753Subproblem 2
x + 16 = -40.398019753 Simplifying x + 16 = -40.398019753 Reorder the terms: 16 + x = -40.398019753 Solving 16 + x = -40.398019753 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 = -40.398019753 + -16 Combine like terms: 16 + -16 = 0 0 + x = -40.398019753 + -16 x = -40.398019753 + -16 Combine like terms: -40.398019753 + -16 = -56.398019753 x = -56.398019753 Simplifying x = -56.398019753Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.398019753, -56.398019753}
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