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Simplifying (16 + r)(16 + r) = r2 + 576 Multiply (16 + r) * (16 + r) (16(16 + r) + r(16 + r)) = r2 + 576 ((16 * 16 + r * 16) + r(16 + r)) = r2 + 576 ((256 + 16r) + r(16 + r)) = r2 + 576 (256 + 16r + (16 * r + r * r)) = r2 + 576 (256 + 16r + (16r + r2)) = r2 + 576 Combine like terms: 16r + 16r = 32r (256 + 32r + r2) = r2 + 576 Reorder the terms: 256 + 32r + r2 = 576 + r2 Add '-1r2' to each side of the equation. 256 + 32r + r2 + -1r2 = 576 + r2 + -1r2 Combine like terms: r2 + -1r2 = 0 256 + 32r + 0 = 576 + r2 + -1r2 256 + 32r = 576 + r2 + -1r2 Combine like terms: r2 + -1r2 = 0 256 + 32r = 576 + 0 256 + 32r = 576 Solving 256 + 32r = 576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-256' to each side of the equation. 256 + -256 + 32r = 576 + -256 Combine like terms: 256 + -256 = 0 0 + 32r = 576 + -256 32r = 576 + -256 Combine like terms: 576 + -256 = 320 32r = 320 Divide each side by '32'. r = 10 Simplifying r = 10
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