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Simplifying 5s2 + -48s + -80 = 0 Reorder the terms: -80 + -48s + 5s2 = 0 Solving -80 + -48s + 5s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + -9.6s + s2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -9.6s + 16 + s2 = 0 + 16 Reorder the terms: -16 + 16 + -9.6s + s2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -9.6s + s2 = 0 + 16 -9.6s + s2 = 0 + 16 Combine like terms: 0 + 16 = 16 -9.6s + s2 = 16 The s term is -9.6s. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6s + 23.04 + s2 = 16 + 23.04 Reorder the terms: 23.04 + -9.6s + s2 = 16 + 23.04 Combine like terms: 16 + 23.04 = 39.04 23.04 + -9.6s + s2 = 39.04 Factor a perfect square on the left side: (s + -4.8)(s + -4.8) = 39.04 Calculate the square root of the right side: 6.248199741 Break this problem into two subproblems by setting (s + -4.8) equal to 6.248199741 and -6.248199741.Subproblem 1
s + -4.8 = 6.248199741 Simplifying s + -4.8 = 6.248199741 Reorder the terms: -4.8 + s = 6.248199741 Solving -4.8 + s = 6.248199741 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + s = 6.248199741 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + s = 6.248199741 + 4.8 s = 6.248199741 + 4.8 Combine like terms: 6.248199741 + 4.8 = 11.048199741 s = 11.048199741 Simplifying s = 11.048199741Subproblem 2
s + -4.8 = -6.248199741 Simplifying s + -4.8 = -6.248199741 Reorder the terms: -4.8 + s = -6.248199741 Solving -4.8 + s = -6.248199741 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + s = -6.248199741 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + s = -6.248199741 + 4.8 s = -6.248199741 + 4.8 Combine like terms: -6.248199741 + 4.8 = -1.448199741 s = -1.448199741 Simplifying s = -1.448199741Solution
The solution to the problem is based on the solutions from the subproblems. s = {11.048199741, -1.448199741}
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