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Simplifying 3s2 + -48s = -123 Reorder the terms: -48s + 3s2 = -123 Solving -48s + 3s2 = -123 Solving for variable 's'. Reorder the terms: 123 + -48s + 3s2 = -123 + 123 Combine like terms: -123 + 123 = 0 123 + -48s + 3s2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(41 + -16s + s2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(41 + -16s + s2)' equal to zero and attempt to solve: Simplifying 41 + -16s + s2 = 0 Solving 41 + -16s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -16s + -41 + s2 = 0 + -41 Reorder the terms: 41 + -41 + -16s + s2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -16s + s2 = 0 + -41 -16s + s2 = 0 + -41 Combine like terms: 0 + -41 = -41 -16s + s2 = -41 The s term is -16s. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16s + 64 + s2 = -41 + 64 Reorder the terms: 64 + -16s + s2 = -41 + 64 Combine like terms: -41 + 64 = 23 64 + -16s + s2 = 23 Factor a perfect square on the left side: (s + -8)(s + -8) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (s + -8) equal to 4.795831523 and -4.795831523.Subproblem 1
s + -8 = 4.795831523 Simplifying s + -8 = 4.795831523 Reorder the terms: -8 + s = 4.795831523 Solving -8 + s = 4.795831523 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + s = 4.795831523 + 8 Combine like terms: -8 + 8 = 0 0 + s = 4.795831523 + 8 s = 4.795831523 + 8 Combine like terms: 4.795831523 + 8 = 12.795831523 s = 12.795831523 Simplifying s = 12.795831523Subproblem 2
s + -8 = -4.795831523 Simplifying s + -8 = -4.795831523 Reorder the terms: -8 + s = -4.795831523 Solving -8 + s = -4.795831523 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + s = -4.795831523 + 8 Combine like terms: -8 + 8 = 0 0 + s = -4.795831523 + 8 s = -4.795831523 + 8 Combine like terms: -4.795831523 + 8 = 3.204168477 s = 3.204168477 Simplifying s = 3.204168477Solution
The solution to the problem is based on the solutions from the subproblems. s = {12.795831523, 3.204168477}Solution
s = {12.795831523, 3.204168477}
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