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Simplifying 0 = s2 + 6s + 10 Reorder the terms: 0 = 10 + 6s + s2 Solving 0 = 10 + 6s + s2 Solving for variable 's'. Combine like terms: 0 + -10 = -10 -10 + -6s + -1s2 = 10 + 6s + s2 + -10 + -6s + -1s2 Reorder the terms: -10 + -6s + -1s2 = 10 + -10 + 6s + -6s + s2 + -1s2 Combine like terms: 10 + -10 = 0 -10 + -6s + -1s2 = 0 + 6s + -6s + s2 + -1s2 -10 + -6s + -1s2 = 6s + -6s + s2 + -1s2 Combine like terms: 6s + -6s = 0 -10 + -6s + -1s2 = 0 + s2 + -1s2 -10 + -6s + -1s2 = s2 + -1s2 Combine like terms: s2 + -1s2 = 0 -10 + -6s + -1s2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 6s + s2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 6s + s2)' equal to zero and attempt to solve: Simplifying 10 + 6s + s2 = 0 Solving 10 + 6s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 6s + -10 + s2 = 0 + -10 Reorder the terms: 10 + -10 + 6s + s2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 6s + s2 = 0 + -10 6s + s2 = 0 + -10 Combine like terms: 0 + -10 = -10 6s + s2 = -10 The s term is 6s. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6s + 9 + s2 = -10 + 9 Reorder the terms: 9 + 6s + s2 = -10 + 9 Combine like terms: -10 + 9 = -1 9 + 6s + s2 = -1 Factor a perfect square on the left side: (s + 3)(s + 3) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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