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Simplifying 3s(s + -2) = 12 Reorder the terms: 3s(-2 + s) = 12 (-2 * 3s + s * 3s) = 12 (-6s + 3s2) = 12 Solving -6s + 3s2 = 12 Solving for variable 's'. Reorder the terms: -12 + -6s + 3s2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -6s + 3s2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -2s + s2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -2s + s2)' equal to zero and attempt to solve: Simplifying -4 + -2s + s2 = 0 Solving -4 + -2s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2s + 4 + s2 = 0 + 4 Reorder the terms: -4 + 4 + -2s + s2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2s + s2 = 0 + 4 -2s + s2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2s + s2 = 4 The s term is -2s. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2s + 1 + s2 = 4 + 1 Reorder the terms: 1 + -2s + s2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2s + s2 = 5 Factor a perfect square on the left side: (s + -1)(s + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (s + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
s + -1 = 2.236067978 Simplifying s + -1 = 2.236067978 Reorder the terms: -1 + s = 2.236067978 Solving -1 + s = 2.236067978 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + s = 2.236067978 + 1 s = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 s = 3.236067978 Simplifying s = 3.236067978Subproblem 2
s + -1 = -2.236067978 Simplifying s + -1 = -2.236067978 Reorder the terms: -1 + s = -2.236067978 Solving -1 + s = -2.236067978 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + s = -2.236067978 + 1 s = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 s = -1.236067978 Simplifying s = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.236067978, -1.236067978}Solution
s = {3.236067978, -1.236067978}
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