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Simplifying 3s2 + -6s + -21 = 0 Reorder the terms: -21 + -6s + 3s2 = 0 Solving -21 + -6s + 3s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -2s + s2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -2s + s2)' equal to zero and attempt to solve: Simplifying -7 + -2s + s2 = 0 Solving -7 + -2s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -2s + 7 + s2 = 0 + 7 Reorder the terms: -7 + 7 + -2s + s2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2s + s2 = 0 + 7 -2s + s2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2s + s2 = 7 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 = 7 + 1 Reorder the terms: 1 + -2s + s2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2s + s2 = 8 Factor a perfect square on the left side: (s + -1)(s + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (s + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
s + -1 = 2.828427125 Simplifying s + -1 = 2.828427125 Reorder the terms: -1 + s = 2.828427125 Solving -1 + s = 2.828427125 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 = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + s = 2.828427125 + 1 s = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 s = 3.828427125 Simplifying s = 3.828427125Subproblem 2
s + -1 = -2.828427125 Simplifying s + -1 = -2.828427125 Reorder the terms: -1 + s = -2.828427125 Solving -1 + s = -2.828427125 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 = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + s = -2.828427125 + 1 s = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 s = -1.828427125 Simplifying s = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.828427125, -1.828427125}Solution
s = {3.828427125, -1.828427125}
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