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Simplifying 25.6 + 4s + -0.1s2 = 0 Solving 25.6 + 4s + -0.1s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -256 + -40s + s2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + -40s + 256 + s2 = 0 + 256 Reorder the terms: -256 + 256 + -40s + s2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -40s + s2 = 0 + 256 -40s + s2 = 0 + 256 Combine like terms: 0 + 256 = 256 -40s + s2 = 256 The s term is -40s. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40s + 400 + s2 = 256 + 400 Reorder the terms: 400 + -40s + s2 = 256 + 400 Combine like terms: 256 + 400 = 656 400 + -40s + s2 = 656 Factor a perfect square on the left side: (s + -20)(s + -20) = 656 Calculate the square root of the right side: 25.61249695 Break this problem into two subproblems by setting (s + -20) equal to 25.61249695 and -25.61249695.Subproblem 1
s + -20 = 25.61249695 Simplifying s + -20 = 25.61249695 Reorder the terms: -20 + s = 25.61249695 Solving -20 + s = 25.61249695 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + s = 25.61249695 + 20 Combine like terms: -20 + 20 = 0 0 + s = 25.61249695 + 20 s = 25.61249695 + 20 Combine like terms: 25.61249695 + 20 = 45.61249695 s = 45.61249695 Simplifying s = 45.61249695Subproblem 2
s + -20 = -25.61249695 Simplifying s + -20 = -25.61249695 Reorder the terms: -20 + s = -25.61249695 Solving -20 + s = -25.61249695 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + s = -25.61249695 + 20 Combine like terms: -20 + 20 = 0 0 + s = -25.61249695 + 20 s = -25.61249695 + 20 Combine like terms: -25.61249695 + 20 = -5.61249695 s = -5.61249695 Simplifying s = -5.61249695Solution
The solution to the problem is based on the solutions from the subproblems. s = {45.61249695, -5.61249695}
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