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Simplifying 5s2 + 10s + -12 + 18s2 + -6s + 13 + s + -5 = 0 Reorder the terms: -12 + 13 + -5 + 10s + -6s + s + 5s2 + 18s2 = 0 Combine like terms: -12 + 13 = 1 1 + -5 + 10s + -6s + s + 5s2 + 18s2 = 0 Combine like terms: 1 + -5 = -4 -4 + 10s + -6s + s + 5s2 + 18s2 = 0 Combine like terms: 10s + -6s = 4s -4 + 4s + s + 5s2 + 18s2 = 0 Combine like terms: 4s + s = 5s -4 + 5s + 5s2 + 18s2 = 0 Combine like terms: 5s2 + 18s2 = 23s2 -4 + 5s + 23s2 = 0 Solving -4 + 5s + 23s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.1739130435 + 0.2173913043s + s2 = 0 Move the constant term to the right: Add '0.1739130435' to each side of the equation. -0.1739130435 + 0.2173913043s + 0.1739130435 + s2 = 0 + 0.1739130435 Reorder the terms: -0.1739130435 + 0.1739130435 + 0.2173913043s + s2 = 0 + 0.1739130435 Combine like terms: -0.1739130435 + 0.1739130435 = 0.0000000000 0.0000000000 + 0.2173913043s + s2 = 0 + 0.1739130435 0.2173913043s + s2 = 0 + 0.1739130435 Combine like terms: 0 + 0.1739130435 = 0.1739130435 0.2173913043s + s2 = 0.1739130435 The s term is 0.2173913043s. Take half its coefficient (0.1086956522). Square it (0.01181474481) and add it to both sides. Add '0.01181474481' to each side of the equation. 0.2173913043s + 0.01181474481 + s2 = 0.1739130435 + 0.01181474481 Reorder the terms: 0.01181474481 + 0.2173913043s + s2 = 0.1739130435 + 0.01181474481 Combine like terms: 0.1739130435 + 0.01181474481 = 0.18572778831 0.01181474481 + 0.2173913043s + s2 = 0.18572778831 Factor a perfect square on the left side: (s + 0.1086956522)(s + 0.1086956522) = 0.18572778831 Calculate the square root of the right side: 0.43096147 Break this problem into two subproblems by setting (s + 0.1086956522) equal to 0.43096147 and -0.43096147.Subproblem 1
s + 0.1086956522 = 0.43096147 Simplifying s + 0.1086956522 = 0.43096147 Reorder the terms: 0.1086956522 + s = 0.43096147 Solving 0.1086956522 + s = 0.43096147 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1086956522' to each side of the equation. 0.1086956522 + -0.1086956522 + s = 0.43096147 + -0.1086956522 Combine like terms: 0.1086956522 + -0.1086956522 = 0.0000000000 0.0000000000 + s = 0.43096147 + -0.1086956522 s = 0.43096147 + -0.1086956522 Combine like terms: 0.43096147 + -0.1086956522 = 0.3222658178 s = 0.3222658178 Simplifying s = 0.3222658178Subproblem 2
s + 0.1086956522 = -0.43096147 Simplifying s + 0.1086956522 = -0.43096147 Reorder the terms: 0.1086956522 + s = -0.43096147 Solving 0.1086956522 + s = -0.43096147 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1086956522' to each side of the equation. 0.1086956522 + -0.1086956522 + s = -0.43096147 + -0.1086956522 Combine like terms: 0.1086956522 + -0.1086956522 = 0.0000000000 0.0000000000 + s = -0.43096147 + -0.1086956522 s = -0.43096147 + -0.1086956522 Combine like terms: -0.43096147 + -0.1086956522 = -0.5396571222 s = -0.5396571222 Simplifying s = -0.5396571222Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.3222658178, -0.5396571222}
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