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Simplifying 125 = 0.005s2 + 1.1s Reorder the terms: 125 = 1.1s + 0.005s2 Solving 125 = 1.1s + 0.005s2 Solving for variable 's'. Reorder the terms: 125 + -1.1s + -0.005s2 = 1.1s + -1.1s + 0.005s2 + -0.005s2 Combine like terms: 1.1s + -1.1s = 0.0 125 + -1.1s + -0.005s2 = 0.0 + 0.005s2 + -0.005s2 125 + -1.1s + -0.005s2 = 0.005s2 + -0.005s2 Combine like terms: 0.005s2 + -0.005s2 = 0.000 125 + -1.1s + -0.005s2 = 0.000 Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. -25000 + 220s + s2 = 0 Move the constant term to the right: Add '25000' to each side of the equation. -25000 + 220s + 25000 + s2 = 0 + 25000 Reorder the terms: -25000 + 25000 + 220s + s2 = 0 + 25000 Combine like terms: -25000 + 25000 = 0 0 + 220s + s2 = 0 + 25000 220s + s2 = 0 + 25000 Combine like terms: 0 + 25000 = 25000 220s + s2 = 25000 The s term is 220s. Take half its coefficient (110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. 220s + 12100 + s2 = 25000 + 12100 Reorder the terms: 12100 + 220s + s2 = 25000 + 12100 Combine like terms: 25000 + 12100 = 37100 12100 + 220s + s2 = 37100 Factor a perfect square on the left side: (s + 110)(s + 110) = 37100 Calculate the square root of the right side: 192.613602843 Break this problem into two subproblems by setting (s + 110) equal to 192.613602843 and -192.613602843.Subproblem 1
s + 110 = 192.613602843 Simplifying s + 110 = 192.613602843 Reorder the terms: 110 + s = 192.613602843 Solving 110 + s = 192.613602843 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -110 + s = 192.613602843 + -110 Combine like terms: 110 + -110 = 0 0 + s = 192.613602843 + -110 s = 192.613602843 + -110 Combine like terms: 192.613602843 + -110 = 82.613602843 s = 82.613602843 Simplifying s = 82.613602843Subproblem 2
s + 110 = -192.613602843 Simplifying s + 110 = -192.613602843 Reorder the terms: 110 + s = -192.613602843 Solving 110 + s = -192.613602843 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -110 + s = -192.613602843 + -110 Combine like terms: 110 + -110 = 0 0 + s = -192.613602843 + -110 s = -192.613602843 + -110 Combine like terms: -192.613602843 + -110 = -302.613602843 s = -302.613602843 Simplifying s = -302.613602843Solution
The solution to the problem is based on the solutions from the subproblems. s = {82.613602843, -302.613602843}
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