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Simplifying 12s2 + 45s + 3 = 0 Reorder the terms: 3 + 45s + 12s2 = 0 Solving 3 + 45s + 12s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 15s + 4s2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 15s + 4s2)' equal to zero and attempt to solve: Simplifying 1 + 15s + 4s2 = 0 Solving 1 + 15s + 4s2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 3.75s + s2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.75s + -0.25 + s2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.75s + s2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.75s + s2 = 0 + -0.25 3.75s + s2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.75s + s2 = -0.25 The s term is 3.75s. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75s + 3.515625 + s2 = -0.25 + 3.515625 Reorder the terms: 3.515625 + 3.75s + s2 = -0.25 + 3.515625 Combine like terms: -0.25 + 3.515625 = 3.265625 3.515625 + 3.75s + s2 = 3.265625 Factor a perfect square on the left side: (s + 1.875)(s + 1.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (s + 1.875) equal to 1.807104037 and -1.807104037.Subproblem 1
s + 1.875 = 1.807104037 Simplifying s + 1.875 = 1.807104037 Reorder the terms: 1.875 + s = 1.807104037 Solving 1.875 + s = 1.807104037 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + s = 1.807104037 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + s = 1.807104037 + -1.875 s = 1.807104037 + -1.875 Combine like terms: 1.807104037 + -1.875 = -0.067895963 s = -0.067895963 Simplifying s = -0.067895963Subproblem 2
s + 1.875 = -1.807104037 Simplifying s + 1.875 = -1.807104037 Reorder the terms: 1.875 + s = -1.807104037 Solving 1.875 + s = -1.807104037 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + s = -1.807104037 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + s = -1.807104037 + -1.875 s = -1.807104037 + -1.875 Combine like terms: -1.807104037 + -1.875 = -3.682104037 s = -3.682104037 Simplifying s = -3.682104037Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.067895963, -3.682104037}Solution
s = {-0.067895963, -3.682104037}
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