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Simplifying 25s2 + 90s = 81 Reorder the terms: 90s + 25s2 = 81 Solving 90s + 25s2 = 81 Solving for variable 's'. Reorder the terms: -81 + 90s + 25s2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 90s + 25s2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.24 + 3.6s + s2 = 0 Move the constant term to the right: Add '3.24' to each side of the equation. -3.24 + 3.6s + 3.24 + s2 = 0 + 3.24 Reorder the terms: -3.24 + 3.24 + 3.6s + s2 = 0 + 3.24 Combine like terms: -3.24 + 3.24 = 0.00 0.00 + 3.6s + s2 = 0 + 3.24 3.6s + s2 = 0 + 3.24 Combine like terms: 0 + 3.24 = 3.24 3.6s + s2 = 3.24 The s term is 3.6s. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6s + 3.24 + s2 = 3.24 + 3.24 Reorder the terms: 3.24 + 3.6s + s2 = 3.24 + 3.24 Combine like terms: 3.24 + 3.24 = 6.48 3.24 + 3.6s + s2 = 6.48 Factor a perfect square on the left side: (s + 1.8)(s + 1.8) = 6.48 Calculate the square root of the right side: 2.545584412 Break this problem into two subproblems by setting (s + 1.8) equal to 2.545584412 and -2.545584412.Subproblem 1
s + 1.8 = 2.545584412 Simplifying s + 1.8 = 2.545584412 Reorder the terms: 1.8 + s = 2.545584412 Solving 1.8 + s = 2.545584412 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + s = 2.545584412 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + s = 2.545584412 + -1.8 s = 2.545584412 + -1.8 Combine like terms: 2.545584412 + -1.8 = 0.745584412 s = 0.745584412 Simplifying s = 0.745584412Subproblem 2
s + 1.8 = -2.545584412 Simplifying s + 1.8 = -2.545584412 Reorder the terms: 1.8 + s = -2.545584412 Solving 1.8 + s = -2.545584412 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + s = -2.545584412 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + s = -2.545584412 + -1.8 s = -2.545584412 + -1.8 Combine like terms: -2.545584412 + -1.8 = -4.345584412 s = -4.345584412 Simplifying s = -4.345584412Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.745584412, -4.345584412}
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