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Simplifying 180 = 0.05s * 0.05s + 11s Reorder the terms for easier multiplication: 180 = 0.05 * 0.05s * s + 11s Multiply 0.05 * 0.05 180 = 0.0025s * s + 11s Multiply s * s 180 = 0.0025s2 + 11s Reorder the terms: 180 = 11s + 0.0025s2 Solving 180 = 11s + 0.0025s2 Solving for variable 's'. Reorder the terms: 180 + -11s + -0.0025s2 = 11s + -11s + 0.0025s2 + -0.0025s2 Combine like terms: 11s + -11s = 0 180 + -11s + -0.0025s2 = 0 + 0.0025s2 + -0.0025s2 180 + -11s + -0.0025s2 = 0.0025s2 + -0.0025s2 Combine like terms: 0.0025s2 + -0.0025s2 = 0.0000 180 + -11s + -0.0025s2 = 0.0000 Begin completing the square. Divide all terms by -0.0025 the coefficient of the squared term: Divide each side by '-0.0025'. -72000 + 4400s + s2 = 0 Move the constant term to the right: Add '72000' to each side of the equation. -72000 + 4400s + 72000 + s2 = 0 + 72000 Reorder the terms: -72000 + 72000 + 4400s + s2 = 0 + 72000 Combine like terms: -72000 + 72000 = 0 0 + 4400s + s2 = 0 + 72000 4400s + s2 = 0 + 72000 Combine like terms: 0 + 72000 = 72000 4400s + s2 = 72000 The s term is 4400s. Take half its coefficient (2200). Square it (4840000) and add it to both sides. Add '4840000' to each side of the equation. 4400s + 4840000 + s2 = 72000 + 4840000 Reorder the terms: 4840000 + 4400s + s2 = 72000 + 4840000 Combine like terms: 72000 + 4840000 = 4912000 4840000 + 4400s + s2 = 4912000 Factor a perfect square on the left side: (s + 2200)(s + 2200) = 4912000 Calculate the square root of the right side: 2216.303228351 Break this problem into two subproblems by setting (s + 2200) equal to 2216.303228351 and -2216.303228351.Subproblem 1
s + 2200 = 2216.303228351 Simplifying s + 2200 = 2216.303228351 Reorder the terms: 2200 + s = 2216.303228351 Solving 2200 + s = 2216.303228351 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2200' to each side of the equation. 2200 + -2200 + s = 2216.303228351 + -2200 Combine like terms: 2200 + -2200 = 0 0 + s = 2216.303228351 + -2200 s = 2216.303228351 + -2200 Combine like terms: 2216.303228351 + -2200 = 16.303228351 s = 16.303228351 Simplifying s = 16.303228351Subproblem 2
s + 2200 = -2216.303228351 Simplifying s + 2200 = -2216.303228351 Reorder the terms: 2200 + s = -2216.303228351 Solving 2200 + s = -2216.303228351 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2200' to each side of the equation. 2200 + -2200 + s = -2216.303228351 + -2200 Combine like terms: 2200 + -2200 = 0 0 + s = -2216.303228351 + -2200 s = -2216.303228351 + -2200 Combine like terms: -2216.303228351 + -2200 = -4416.303228351 s = -4416.303228351 Simplifying s = -4416.303228351Solution
The solution to the problem is based on the solutions from the subproblems. s = {16.303228351, -4416.303228351}
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