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Simplifying 3 = t2 + -3t + -10 Reorder the terms: 3 = -10 + -3t + t2 Solving 3 = -10 + -3t + t2 Solving for variable 't'. Combine like terms: 3 + 10 = 13 13 + 3t + -1t2 = -10 + -3t + t2 + 10 + 3t + -1t2 Reorder the terms: 13 + 3t + -1t2 = -10 + 10 + -3t + 3t + t2 + -1t2 Combine like terms: -10 + 10 = 0 13 + 3t + -1t2 = 0 + -3t + 3t + t2 + -1t2 13 + 3t + -1t2 = -3t + 3t + t2 + -1t2 Combine like terms: -3t + 3t = 0 13 + 3t + -1t2 = 0 + t2 + -1t2 13 + 3t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 13 + 3t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -3t + t2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -3t + 13 + t2 = 0 + 13 Reorder the terms: -13 + 13 + -3t + t2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3t + t2 = 0 + 13 -3t + t2 = 0 + 13 Combine like terms: 0 + 13 = 13 -3t + t2 = 13 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 13 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 13 + 2.25 Combine like terms: 13 + 2.25 = 15.25 2.25 + -3t + t2 = 15.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (t + -1.5) equal to 3.905124838 and -3.905124838.Subproblem 1
t + -1.5 = 3.905124838 Simplifying t + -1.5 = 3.905124838 Reorder the terms: -1.5 + t = 3.905124838 Solving -1.5 + t = 3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 3.905124838 + 1.5 t = 3.905124838 + 1.5 Combine like terms: 3.905124838 + 1.5 = 5.405124838 t = 5.405124838 Simplifying t = 5.405124838Subproblem 2
t + -1.5 = -3.905124838 Simplifying t + -1.5 = -3.905124838 Reorder the terms: -1.5 + t = -3.905124838 Solving -1.5 + t = -3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -3.905124838 + 1.5 t = -3.905124838 + 1.5 Combine like terms: -3.905124838 + 1.5 = -2.405124838 t = -2.405124838 Simplifying t = -2.405124838Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.405124838, -2.405124838}
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