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Simplifying s2 + -32s + 6 = 0 Reorder the terms: 6 + -32s + s2 = 0 Solving 6 + -32s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -32s + -6 + s2 = 0 + -6 Reorder the terms: 6 + -6 + -32s + s2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -32s + s2 = 0 + -6 -32s + s2 = 0 + -6 Combine like terms: 0 + -6 = -6 -32s + s2 = -6 The s term is -32s. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32s + 256 + s2 = -6 + 256 Reorder the terms: 256 + -32s + s2 = -6 + 256 Combine like terms: -6 + 256 = 250 256 + -32s + s2 = 250 Factor a perfect square on the left side: (s + -16)(s + -16) = 250 Calculate the square root of the right side: 15.811388301 Break this problem into two subproblems by setting (s + -16) equal to 15.811388301 and -15.811388301.Subproblem 1
s + -16 = 15.811388301 Simplifying s + -16 = 15.811388301 Reorder the terms: -16 + s = 15.811388301 Solving -16 + s = 15.811388301 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + s = 15.811388301 + 16 Combine like terms: -16 + 16 = 0 0 + s = 15.811388301 + 16 s = 15.811388301 + 16 Combine like terms: 15.811388301 + 16 = 31.811388301 s = 31.811388301 Simplifying s = 31.811388301Subproblem 2
s + -16 = -15.811388301 Simplifying s + -16 = -15.811388301 Reorder the terms: -16 + s = -15.811388301 Solving -16 + s = -15.811388301 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + s = -15.811388301 + 16 Combine like terms: -16 + 16 = 0 0 + s = -15.811388301 + 16 s = -15.811388301 + 16 Combine like terms: -15.811388301 + 16 = 0.188611699 s = 0.188611699 Simplifying s = 0.188611699Solution
The solution to the problem is based on the solutions from the subproblems. s = {31.811388301, 0.188611699}
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