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Simplifying 0 = -4(r + 8)(r + 8) Reorder the terms: 0 = -4(8 + r)(r + 8) Reorder the terms: 0 = -4(8 + r)(8 + r) Multiply (8 + r) * (8 + r) 0 = -4(8(8 + r) + r(8 + r)) 0 = -4((8 * 8 + r * 8) + r(8 + r)) 0 = -4((64 + 8r) + r(8 + r)) 0 = -4(64 + 8r + (8 * r + r * r)) 0 = -4(64 + 8r + (8r + r2)) Combine like terms: 8r + 8r = 16r 0 = -4(64 + 16r + r2) 0 = (64 * -4 + 16r * -4 + r2 * -4) 0 = (-256 + -64r + -4r2) Solving 0 = -256 + -64r + -4r2 Solving for variable 'r'. Combine like terms: 0 + 256 = 256 256 + 64r + 4r2 = -256 + -64r + -4r2 + 256 + 64r + 4r2 Reorder the terms: 256 + 64r + 4r2 = -256 + 256 + -64r + 64r + -4r2 + 4r2 Combine like terms: -256 + 256 = 0 256 + 64r + 4r2 = 0 + -64r + 64r + -4r2 + 4r2 256 + 64r + 4r2 = -64r + 64r + -4r2 + 4r2 Combine like terms: -64r + 64r = 0 256 + 64r + 4r2 = 0 + -4r2 + 4r2 256 + 64r + 4r2 = -4r2 + 4r2 Combine like terms: -4r2 + 4r2 = 0 256 + 64r + 4r2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(64 + 16r + r2) = 0 Factor a trinomial. 4((8 + r)(8 + r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve: Simplifying 8 + r = 0 Solving 8 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + r = 0 + -8 r = 0 + -8 Combine like terms: 0 + -8 = -8 r = -8 Simplifying r = -8Subproblem 2
Set the factor '(8 + r)' equal to zero and attempt to solve: Simplifying 8 + r = 0 Solving 8 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + r = 0 + -8 r = 0 + -8 Combine like terms: 0 + -8 = -8 r = -8 Simplifying r = -8Solution
r = {-8, -8}
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