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Simplifying 16s2 + 24s + -9 = 0 Reorder the terms: -9 + 24s + 16s2 = 0 Solving -9 + 24s + 16s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + 1.5s + s2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 1.5s + 0.5625 + s2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 1.5s + s2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 1.5s + s2 = 0 + 0.5625 1.5s + s2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 1.5s + s2 = 0.5625 The s term is 1.5s. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5s + 0.5625 + s2 = 0.5625 + 0.5625 Reorder the terms: 0.5625 + 1.5s + s2 = 0.5625 + 0.5625 Combine like terms: 0.5625 + 0.5625 = 1.125 0.5625 + 1.5s + s2 = 1.125 Factor a perfect square on the left side: (s + 0.75)(s + 0.75) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (s + 0.75) equal to 1.060660172 and -1.060660172.Subproblem 1
s + 0.75 = 1.060660172 Simplifying s + 0.75 = 1.060660172 Reorder the terms: 0.75 + s = 1.060660172 Solving 0.75 + s = 1.060660172 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = 1.060660172 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = 1.060660172 + -0.75 s = 1.060660172 + -0.75 Combine like terms: 1.060660172 + -0.75 = 0.310660172 s = 0.310660172 Simplifying s = 0.310660172Subproblem 2
s + 0.75 = -1.060660172 Simplifying s + 0.75 = -1.060660172 Reorder the terms: 0.75 + s = -1.060660172 Solving 0.75 + s = -1.060660172 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = -1.060660172 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = -1.060660172 + -0.75 s = -1.060660172 + -0.75 Combine like terms: -1.060660172 + -0.75 = -1.810660172 s = -1.810660172 Simplifying s = -1.810660172Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.310660172, -1.810660172}
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