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Simplifying (4 + s)(s) = 100 Reorder the terms for easier multiplication: s(4 + s) = 100 (4 * s + s * s) = 100 (4s + s2) = 100 Solving 4s + s2 = 100 Solving for variable 's'. Reorder the terms: -100 + 4s + s2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 4s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 4s + 100 + s2 = 0 + 100 Reorder the terms: -100 + 100 + 4s + s2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 4s + s2 = 0 + 100 4s + s2 = 0 + 100 Combine like terms: 0 + 100 = 100 4s + s2 = 100 The s term is 4s. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4s + 4 + s2 = 100 + 4 Reorder the terms: 4 + 4s + s2 = 100 + 4 Combine like terms: 100 + 4 = 104 4 + 4s + s2 = 104 Factor a perfect square on the left side: (s + 2)(s + 2) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (s + 2) equal to 10.198039027 and -10.198039027.Subproblem 1
s + 2 = 10.198039027 Simplifying s + 2 = 10.198039027 Reorder the terms: 2 + s = 10.198039027 Solving 2 + s = 10.198039027 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + s = 10.198039027 + -2 s = 10.198039027 + -2 Combine like terms: 10.198039027 + -2 = 8.198039027 s = 8.198039027 Simplifying s = 8.198039027Subproblem 2
s + 2 = -10.198039027 Simplifying s + 2 = -10.198039027 Reorder the terms: 2 + s = -10.198039027 Solving 2 + s = -10.198039027 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + s = -10.198039027 + -2 s = -10.198039027 + -2 Combine like terms: -10.198039027 + -2 = -12.198039027 s = -12.198039027 Simplifying s = -12.198039027Solution
The solution to the problem is based on the solutions from the subproblems. s = {8.198039027, -12.198039027}
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