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Simplifying 3s2 + 48s + 99 = 0 Reorder the terms: 99 + 48s + 3s2 = 0 Solving 99 + 48s + 3s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '3'. 3(33 + 16s + s2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(33 + 16s + s2)' equal to zero and attempt to solve: Simplifying 33 + 16s + s2 = 0 Solving 33 + 16s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 16s + -33 + s2 = 0 + -33 Reorder the terms: 33 + -33 + 16s + s2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 16s + s2 = 0 + -33 16s + s2 = 0 + -33 Combine like terms: 0 + -33 = -33 16s + s2 = -33 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 = -33 + 64 Reorder the terms: 64 + 16s + s2 = -33 + 64 Combine like terms: -33 + 64 = 31 64 + 16s + s2 = 31 Factor a perfect square on the left side: (s + 8)(s + 8) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (s + 8) equal to 5.567764363 and -5.567764363.Subproblem 1
s + 8 = 5.567764363 Simplifying s + 8 = 5.567764363 Reorder the terms: 8 + s = 5.567764363 Solving 8 + s = 5.567764363 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 = 5.567764363 + -8 Combine like terms: 8 + -8 = 0 0 + s = 5.567764363 + -8 s = 5.567764363 + -8 Combine like terms: 5.567764363 + -8 = -2.432235637 s = -2.432235637 Simplifying s = -2.432235637Subproblem 2
s + 8 = -5.567764363 Simplifying s + 8 = -5.567764363 Reorder the terms: 8 + s = -5.567764363 Solving 8 + s = -5.567764363 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 = -5.567764363 + -8 Combine like terms: 8 + -8 = 0 0 + s = -5.567764363 + -8 s = -5.567764363 + -8 Combine like terms: -5.567764363 + -8 = -13.567764363 s = -13.567764363 Simplifying s = -13.567764363Solution
The solution to the problem is based on the solutions from the subproblems. s = {-2.432235637, -13.567764363}Solution
s = {-2.432235637, -13.567764363}
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