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Simplifying 8s + -11 = (s + -4)(s + -2) Reorder the terms: -11 + 8s = (s + -4)(s + -2) Reorder the terms: -11 + 8s = (-4 + s)(s + -2) Reorder the terms: -11 + 8s = (-4 + s)(-2 + s) Multiply (-4 + s) * (-2 + s) -11 + 8s = (-4(-2 + s) + s(-2 + s)) -11 + 8s = ((-2 * -4 + s * -4) + s(-2 + s)) -11 + 8s = ((8 + -4s) + s(-2 + s)) -11 + 8s = (8 + -4s + (-2 * s + s * s)) -11 + 8s = (8 + -4s + (-2s + s2)) Combine like terms: -4s + -2s = -6s -11 + 8s = (8 + -6s + s2) Solving -11 + 8s = 8 + -6s + s2 Solving for variable 's'. Reorder the terms: -11 + -8 + 8s + 6s + -1s2 = 8 + -6s + s2 + -8 + 6s + -1s2 Combine like terms: -11 + -8 = -19 -19 + 8s + 6s + -1s2 = 8 + -6s + s2 + -8 + 6s + -1s2 Combine like terms: 8s + 6s = 14s -19 + 14s + -1s2 = 8 + -6s + s2 + -8 + 6s + -1s2 Reorder the terms: -19 + 14s + -1s2 = 8 + -8 + -6s + 6s + s2 + -1s2 Combine like terms: 8 + -8 = 0 -19 + 14s + -1s2 = 0 + -6s + 6s + s2 + -1s2 -19 + 14s + -1s2 = -6s + 6s + s2 + -1s2 Combine like terms: -6s + 6s = 0 -19 + 14s + -1s2 = 0 + s2 + -1s2 -19 + 14s + -1s2 = s2 + -1s2 Combine like terms: s2 + -1s2 = 0 -19 + 14s + -1s2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 19 + -14s + s2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + -14s + -19 + s2 = 0 + -19 Reorder the terms: 19 + -19 + -14s + s2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -14s + s2 = 0 + -19 -14s + s2 = 0 + -19 Combine like terms: 0 + -19 = -19 -14s + s2 = -19 The s term is -14s. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14s + 49 + s2 = -19 + 49 Reorder the terms: 49 + -14s + s2 = -19 + 49 Combine like terms: -19 + 49 = 30 49 + -14s + s2 = 30 Factor a perfect square on the left side: (s + -7)(s + -7) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (s + -7) equal to 5.477225575 and -5.477225575.Subproblem 1
s + -7 = 5.477225575 Simplifying s + -7 = 5.477225575 Reorder the terms: -7 + s = 5.477225575 Solving -7 + s = 5.477225575 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = 5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + s = 5.477225575 + 7 s = 5.477225575 + 7 Combine like terms: 5.477225575 + 7 = 12.477225575 s = 12.477225575 Simplifying s = 12.477225575Subproblem 2
s + -7 = -5.477225575 Simplifying s + -7 = -5.477225575 Reorder the terms: -7 + s = -5.477225575 Solving -7 + s = -5.477225575 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = -5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + s = -5.477225575 + 7 s = -5.477225575 + 7 Combine like terms: -5.477225575 + 7 = 1.522774425 s = 1.522774425 Simplifying s = 1.522774425Solution
The solution to the problem is based on the solutions from the subproblems. s = {12.477225575, 1.522774425}
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