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Simplifying (8r + -4)(8r + -4) = 0 Reorder the terms: (-4 + 8r)(8r + -4) = 0 Reorder the terms: (-4 + 8r)(-4 + 8r) = 0 Multiply (-4 + 8r) * (-4 + 8r) (-4(-4 + 8r) + 8r * (-4 + 8r)) = 0 ((-4 * -4 + 8r * -4) + 8r * (-4 + 8r)) = 0 ((16 + -32r) + 8r * (-4 + 8r)) = 0 (16 + -32r + (-4 * 8r + 8r * 8r)) = 0 (16 + -32r + (-32r + 64r2)) = 0 Combine like terms: -32r + -32r = -64r (16 + -64r + 64r2) = 0 Solving 16 + -64r + 64r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '16'. 16(1 + -4r + 4r2) = 0 Factor a trinomial. 16((1 + -2r)(1 + -2r)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Solution
r = {0.5, 0.5}
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