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Simplifying s = 2(s + 3) * 4s + -5 Reorder the terms: s = 2(3 + s) * 4s + -5 Reorder the terms for easier multiplication: s = 2 * 4s(3 + s) + -5 Multiply 2 * 4 s = 8s(3 + s) + -5 s = (3 * 8s + s * 8s) + -5 s = (24s + 8s2) + -5 Reorder the terms: s = -5 + 24s + 8s2 Solving s = -5 + 24s + 8s2 Solving for variable 's'. Reorder the terms: 5 + s + -24s + -8s2 = -5 + 24s + 8s2 + 5 + -24s + -8s2 Combine like terms: s + -24s = -23s 5 + -23s + -8s2 = -5 + 24s + 8s2 + 5 + -24s + -8s2 Reorder the terms: 5 + -23s + -8s2 = -5 + 5 + 24s + -24s + 8s2 + -8s2 Combine like terms: -5 + 5 = 0 5 + -23s + -8s2 = 0 + 24s + -24s + 8s2 + -8s2 5 + -23s + -8s2 = 24s + -24s + 8s2 + -8s2 Combine like terms: 24s + -24s = 0 5 + -23s + -8s2 = 0 + 8s2 + -8s2 5 + -23s + -8s2 = 8s2 + -8s2 Combine like terms: 8s2 + -8s2 = 0 5 + -23s + -8s2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + 2.875s + s2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 2.875s + 0.625 + s2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 2.875s + s2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 2.875s + s2 = 0 + 0.625 2.875s + s2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 2.875s + s2 = 0.625 The s term is 2.875s. Take half its coefficient (1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. 2.875s + 2.06640625 + s2 = 0.625 + 2.06640625 Reorder the terms: 2.06640625 + 2.875s + s2 = 0.625 + 2.06640625 Combine like terms: 0.625 + 2.06640625 = 2.69140625 2.06640625 + 2.875s + s2 = 2.69140625 Factor a perfect square on the left side: (s + 1.4375)(s + 1.4375) = 2.69140625 Calculate the square root of the right side: 1.640550594 Break this problem into two subproblems by setting (s + 1.4375) equal to 1.640550594 and -1.640550594.Subproblem 1
s + 1.4375 = 1.640550594 Simplifying s + 1.4375 = 1.640550594 Reorder the terms: 1.4375 + s = 1.640550594 Solving 1.4375 + s = 1.640550594 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + s = 1.640550594 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + s = 1.640550594 + -1.4375 s = 1.640550594 + -1.4375 Combine like terms: 1.640550594 + -1.4375 = 0.203050594 s = 0.203050594 Simplifying s = 0.203050594Subproblem 2
s + 1.4375 = -1.640550594 Simplifying s + 1.4375 = -1.640550594 Reorder the terms: 1.4375 + s = -1.640550594 Solving 1.4375 + s = -1.640550594 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + s = -1.640550594 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + s = -1.640550594 + -1.4375 s = -1.640550594 + -1.4375 Combine like terms: -1.640550594 + -1.4375 = -3.078050594 s = -3.078050594 Simplifying s = -3.078050594Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.203050594, -3.078050594}
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