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Simplifying 100 = 0.05s2 + 2.1s Reorder the terms: 100 = 2.1s + 0.05s2 Solving 100 = 2.1s + 0.05s2 Solving for variable 's'. Reorder the terms: 100 + -2.1s + -0.05s2 = 2.1s + -2.1s + 0.05s2 + -0.05s2 Combine like terms: 2.1s + -2.1s = 0.0 100 + -2.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2 100 + -2.1s + -0.05s2 = 0.05s2 + -0.05s2 Combine like terms: 0.05s2 + -0.05s2 = 0.00 100 + -2.1s + -0.05s2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -2000 + 42s + s2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 42s + 2000 + s2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 42s + s2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 42s + s2 = 0 + 2000 42s + s2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 42s + s2 = 2000 The s term is 42s. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42s + 441 + s2 = 2000 + 441 Reorder the terms: 441 + 42s + s2 = 2000 + 441 Combine like terms: 2000 + 441 = 2441 441 + 42s + s2 = 2441 Factor a perfect square on the left side: (s + 21)(s + 21) = 2441 Calculate the square root of the right side: 49.406477308 Break this problem into two subproblems by setting (s + 21) equal to 49.406477308 and -49.406477308.Subproblem 1
s + 21 = 49.406477308 Simplifying s + 21 = 49.406477308 Reorder the terms: 21 + s = 49.406477308 Solving 21 + s = 49.406477308 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + s = 49.406477308 + -21 Combine like terms: 21 + -21 = 0 0 + s = 49.406477308 + -21 s = 49.406477308 + -21 Combine like terms: 49.406477308 + -21 = 28.406477308 s = 28.406477308 Simplifying s = 28.406477308Subproblem 2
s + 21 = -49.406477308 Simplifying s + 21 = -49.406477308 Reorder the terms: 21 + s = -49.406477308 Solving 21 + s = -49.406477308 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + s = -49.406477308 + -21 Combine like terms: 21 + -21 = 0 0 + s = -49.406477308 + -21 s = -49.406477308 + -21 Combine like terms: -49.406477308 + -21 = -70.406477308 s = -70.406477308 Simplifying s = -70.406477308Solution
The solution to the problem is based on the solutions from the subproblems. s = {28.406477308, -70.406477308}
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