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Simplifying 7(s + 3)(s + 3) + -41(s + 3) = 6 Reorder the terms: 7(3 + s)(s + 3) + -41(s + 3) = 6 Reorder the terms: 7(3 + s)(3 + s) + -41(s + 3) = 6 Multiply (3 + s) * (3 + s) 7(3(3 + s) + s(3 + s)) + -41(s + 3) = 6 7((3 * 3 + s * 3) + s(3 + s)) + -41(s + 3) = 6 7((9 + 3s) + s(3 + s)) + -41(s + 3) = 6 7(9 + 3s + (3 * s + s * s)) + -41(s + 3) = 6 7(9 + 3s + (3s + s2)) + -41(s + 3) = 6 Combine like terms: 3s + 3s = 6s 7(9 + 6s + s2) + -41(s + 3) = 6 (9 * 7 + 6s * 7 + s2 * 7) + -41(s + 3) = 6 (63 + 42s + 7s2) + -41(s + 3) = 6 Reorder the terms: 63 + 42s + 7s2 + -41(3 + s) = 6 63 + 42s + 7s2 + (3 * -41 + s * -41) = 6 63 + 42s + 7s2 + (-123 + -41s) = 6 Reorder the terms: 63 + -123 + 42s + -41s + 7s2 = 6 Combine like terms: 63 + -123 = -60 -60 + 42s + -41s + 7s2 = 6 Combine like terms: 42s + -41s = 1s -60 + 1s + 7s2 = 6 Solving -60 + 1s + 7s2 = 6 Solving for variable 's'. Reorder the terms: -60 + -6 + 1s + 7s2 = 6 + -6 Combine like terms: -60 + -6 = -66 -66 + 1s + 7s2 = 6 + -6 Combine like terms: 6 + -6 = 0 -66 + 1s + 7s2 = 0 Factor a trinomial. (-22 + -7s)(3 + -1s) = 0Subproblem 1
Set the factor '(-22 + -7s)' equal to zero and attempt to solve: Simplifying -22 + -7s = 0 Solving -22 + -7s = 0 Move all terms containing s to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + -7s = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -7s = 0 + 22 -7s = 0 + 22 Combine like terms: 0 + 22 = 22 -7s = 22 Divide each side by '-7'. s = -3.142857143 Simplifying s = -3.142857143Subproblem 2
Set the factor '(3 + -1s)' equal to zero and attempt to solve: Simplifying 3 + -1s = 0 Solving 3 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1s = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1s = 0 + -3 -1s = 0 + -3 Combine like terms: 0 + -3 = -3 -1s = -3 Divide each side by '-1'. s = 3 Simplifying s = 3Solution
s = {-3.142857143, 3}
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