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Simplifying 4s2 + 16s = 148 Reorder the terms: 16s + 4s2 = 148 Solving 16s + 4s2 = 148 Solving for variable 's'. Reorder the terms: -148 + 16s + 4s2 = 148 + -148 Combine like terms: 148 + -148 = 0 -148 + 16s + 4s2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-37 + 4s + s2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-37 + 4s + s2)' equal to zero and attempt to solve: Simplifying -37 + 4s + s2 = 0 Solving -37 + 4s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 4s + 37 + s2 = 0 + 37 Reorder the terms: -37 + 37 + 4s + s2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 4s + s2 = 0 + 37 4s + s2 = 0 + 37 Combine like terms: 0 + 37 = 37 4s + s2 = 37 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 = 37 + 4 Reorder the terms: 4 + 4s + s2 = 37 + 4 Combine like terms: 37 + 4 = 41 4 + 4s + s2 = 41 Factor a perfect square on the left side: (s + 2)(s + 2) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (s + 2) equal to 6.403124237 and -6.403124237.Subproblem 1
s + 2 = 6.403124237 Simplifying s + 2 = 6.403124237 Reorder the terms: 2 + s = 6.403124237 Solving 2 + s = 6.403124237 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 = 6.403124237 + -2 Combine like terms: 2 + -2 = 0 0 + s = 6.403124237 + -2 s = 6.403124237 + -2 Combine like terms: 6.403124237 + -2 = 4.403124237 s = 4.403124237 Simplifying s = 4.403124237Subproblem 2
s + 2 = -6.403124237 Simplifying s + 2 = -6.403124237 Reorder the terms: 2 + s = -6.403124237 Solving 2 + s = -6.403124237 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 = -6.403124237 + -2 Combine like terms: 2 + -2 = 0 0 + s = -6.403124237 + -2 s = -6.403124237 + -2 Combine like terms: -6.403124237 + -2 = -8.403124237 s = -8.403124237 Simplifying s = -8.403124237Solution
The solution to the problem is based on the solutions from the subproblems. s = {4.403124237, -8.403124237}Solution
s = {4.403124237, -8.403124237}
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