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Simplifying 0 = 4f2 + 32f + 63 Reorder the terms: 0 = 63 + 32f + 4f2 Solving 0 = 63 + 32f + 4f2 Solving for variable 'f'. Combine like terms: 0 + -63 = -63 -63 + -32f + -4f2 = 63 + 32f + 4f2 + -63 + -32f + -4f2 Reorder the terms: -63 + -32f + -4f2 = 63 + -63 + 32f + -32f + 4f2 + -4f2 Combine like terms: 63 + -63 = 0 -63 + -32f + -4f2 = 0 + 32f + -32f + 4f2 + -4f2 -63 + -32f + -4f2 = 32f + -32f + 4f2 + -4f2 Combine like terms: 32f + -32f = 0 -63 + -32f + -4f2 = 0 + 4f2 + -4f2 -63 + -32f + -4f2 = 4f2 + -4f2 Combine like terms: 4f2 + -4f2 = 0 -63 + -32f + -4f2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(63 + 32f + 4f2) = 0 Factor a trinomial. -1((9 + 2f)(7 + 2f)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 2f)' equal to zero and attempt to solve: Simplifying 9 + 2f = 0 Solving 9 + 2f = 0 Move all terms containing f to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2f = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2f = 0 + -9 2f = 0 + -9 Combine like terms: 0 + -9 = -9 2f = -9 Divide each side by '2'. f = -4.5 Simplifying f = -4.5Subproblem 2
Set the factor '(7 + 2f)' equal to zero and attempt to solve: Simplifying 7 + 2f = 0 Solving 7 + 2f = 0 Move all terms containing f to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2f = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2f = 0 + -7 2f = 0 + -7 Combine like terms: 0 + -7 = -7 2f = -7 Divide each side by '2'. f = -3.5 Simplifying f = -3.5Solution
f = {-4.5, -3.5}
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