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Simplifying s2 + 15s + 20 = 0 Reorder the terms: 20 + 15s + s2 = 0 Solving 20 + 15s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 15s + -20 + s2 = 0 + -20 Reorder the terms: 20 + -20 + 15s + s2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 15s + s2 = 0 + -20 15s + s2 = 0 + -20 Combine like terms: 0 + -20 = -20 15s + s2 = -20 The s term is 15s. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15s + 56.25 + s2 = -20 + 56.25 Reorder the terms: 56.25 + 15s + s2 = -20 + 56.25 Combine like terms: -20 + 56.25 = 36.25 56.25 + 15s + s2 = 36.25 Factor a perfect square on the left side: (s + 7.5)(s + 7.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (s + 7.5) equal to 6.020797289 and -6.020797289.Subproblem 1
s + 7.5 = 6.020797289 Simplifying s + 7.5 = 6.020797289 Reorder the terms: 7.5 + s = 6.020797289 Solving 7.5 + s = 6.020797289 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + s = 6.020797289 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + s = 6.020797289 + -7.5 s = 6.020797289 + -7.5 Combine like terms: 6.020797289 + -7.5 = -1.479202711 s = -1.479202711 Simplifying s = -1.479202711Subproblem 2
s + 7.5 = -6.020797289 Simplifying s + 7.5 = -6.020797289 Reorder the terms: 7.5 + s = -6.020797289 Solving 7.5 + s = -6.020797289 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + s = -6.020797289 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + s = -6.020797289 + -7.5 s = -6.020797289 + -7.5 Combine like terms: -6.020797289 + -7.5 = -13.520797289 s = -13.520797289 Simplifying s = -13.520797289Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.479202711, -13.520797289}
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