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Simplifying 1200 = s2 + 6s Reorder the terms: 1200 = 6s + s2 Solving 1200 = 6s + s2 Solving for variable 's'. Reorder the terms: 1200 + -6s + -1s2 = 6s + -6s + s2 + -1s2 Combine like terms: 6s + -6s = 0 1200 + -6s + -1s2 = 0 + s2 + -1s2 1200 + -6s + -1s2 = s2 + -1s2 Combine like terms: s2 + -1s2 = 0 1200 + -6s + -1s2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1200 + 6s + s2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 6s + 1200 + s2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 6s + s2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 6s + s2 = 0 + 1200 6s + s2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 6s + s2 = 1200 The s term is 6s. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6s + 9 + s2 = 1200 + 9 Reorder the terms: 9 + 6s + s2 = 1200 + 9 Combine like terms: 1200 + 9 = 1209 9 + 6s + s2 = 1209 Factor a perfect square on the left side: (s + 3)(s + 3) = 1209 Calculate the square root of the right side: 34.770677301 Break this problem into two subproblems by setting (s + 3) equal to 34.770677301 and -34.770677301.Subproblem 1
s + 3 = 34.770677301 Simplifying s + 3 = 34.770677301 Reorder the terms: 3 + s = 34.770677301 Solving 3 + s = 34.770677301 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = 34.770677301 + -3 Combine like terms: 3 + -3 = 0 0 + s = 34.770677301 + -3 s = 34.770677301 + -3 Combine like terms: 34.770677301 + -3 = 31.770677301 s = 31.770677301 Simplifying s = 31.770677301Subproblem 2
s + 3 = -34.770677301 Simplifying s + 3 = -34.770677301 Reorder the terms: 3 + s = -34.770677301 Solving 3 + s = -34.770677301 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = -34.770677301 + -3 Combine like terms: 3 + -3 = 0 0 + s = -34.770677301 + -3 s = -34.770677301 + -3 Combine like terms: -34.770677301 + -3 = -37.770677301 s = -37.770677301 Simplifying s = -37.770677301Solution
The solution to the problem is based on the solutions from the subproblems. s = {31.770677301, -37.770677301}
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