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Simplifying 0 = 4t2 + -10t + 13 Reorder the terms: 0 = 13 + -10t + 4t2 Solving 0 = 13 + -10t + 4t2 Solving for variable 't'. Combine like terms: 0 + -13 = -13 -13 + 10t + -4t2 = 13 + -10t + 4t2 + -13 + 10t + -4t2 Reorder the terms: -13 + 10t + -4t2 = 13 + -13 + -10t + 10t + 4t2 + -4t2 Combine like terms: 13 + -13 = 0 -13 + 10t + -4t2 = 0 + -10t + 10t + 4t2 + -4t2 -13 + 10t + -4t2 = -10t + 10t + 4t2 + -4t2 Combine like terms: -10t + 10t = 0 -13 + 10t + -4t2 = 0 + 4t2 + -4t2 -13 + 10t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -13 + 10t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.25 + -2.5t + t2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -2.5t + -3.25 + t2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -2.5t + t2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -2.5t + t2 = 0 + -3.25 -2.5t + t2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -2.5t + t2 = -3.25 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = -3.25 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = -3.25 + 1.5625 Combine like terms: -3.25 + 1.5625 = -1.6875 1.5625 + -2.5t + t2 = -1.6875 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = -1.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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