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Simplifying 3t2 + 6t + 15 = 0 Reorder the terms: 15 + 6t + 3t2 = 0 Solving 15 + 6t + 3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 2t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 2t + t2)' equal to zero and attempt to solve: Simplifying 5 + 2t + t2 = 0 Solving 5 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 2t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + 2t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2t + t2 = 0 + -5 2t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 2t + t2 = -5 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = -5 + 1 Reorder the terms: 1 + 2t + t2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + 2t + t2 = -4 Factor a perfect square on the left side: (t + 1)(t + 1) = -4 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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