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Simplifying (10r + -4)(10r + -4) = 0 Reorder the terms: (-4 + 10r)(10r + -4) = 0 Reorder the terms: (-4 + 10r)(-4 + 10r) = 0 Multiply (-4 + 10r) * (-4 + 10r) (-4(-4 + 10r) + 10r * (-4 + 10r)) = 0 ((-4 * -4 + 10r * -4) + 10r * (-4 + 10r)) = 0 ((16 + -40r) + 10r * (-4 + 10r)) = 0 (16 + -40r + (-4 * 10r + 10r * 10r)) = 0 (16 + -40r + (-40r + 100r2)) = 0 Combine like terms: -40r + -40r = -80r (16 + -80r + 100r2) = 0 Solving 16 + -80r + 100r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -20r + 25r2) = 0 Factor a trinomial. 4((2 + -5r)(2 + -5r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -5r)' equal to zero and attempt to solve: Simplifying 2 + -5r = 0 Solving 2 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5r = 0 + -2 -5r = 0 + -2 Combine like terms: 0 + -2 = -2 -5r = -2 Divide each side by '-5'. r = 0.4 Simplifying r = 0.4Subproblem 2
Set the factor '(2 + -5r)' equal to zero and attempt to solve: Simplifying 2 + -5r = 0 Solving 2 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5r = 0 + -2 -5r = 0 + -2 Combine like terms: 0 + -2 = -2 -5r = -2 Divide each side by '-5'. r = 0.4 Simplifying r = 0.4Solution
r = {0.4, 0.4}
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