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Simplifying 0 = 5t2 + -10t + 15 Reorder the terms: 0 = 15 + -10t + 5t2 Solving 0 = 15 + -10t + 5t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + 10t + -5t2 = 15 + -10t + 5t2 + -15 + 10t + -5t2 Reorder the terms: -15 + 10t + -5t2 = 15 + -15 + -10t + 10t + 5t2 + -5t2 Combine like terms: 15 + -15 = 0 -15 + 10t + -5t2 = 0 + -10t + 10t + 5t2 + -5t2 -15 + 10t + -5t2 = -10t + 10t + 5t2 + -5t2 Combine like terms: -10t + 10t = 0 -15 + 10t + -5t2 = 0 + 5t2 + -5t2 -15 + 10t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 -15 + 10t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 2t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + 2t + -1t2)' equal to zero and attempt to solve: Simplifying -3 + 2t + -1t2 = 0 Solving -3 + 2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -2t + t2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -2t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t + t2 = 0 + -3 -2t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2t + t2 = -3 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 = -3 + 1 Reorder the terms: 1 + -2t + t2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2t + t2 = -2 Factor a perfect square on the left side: (t + -1)(t + -1) = -2 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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