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Simplifying -3t2 + 15t + 13 = 0 Reorder the terms: 13 + 15t + -3t2 = 0 Solving 13 + 15t + -3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4.333333333 + -5t + t2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -5t + 4.333333333 + t2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -5t + t2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -5t + t2 = 0 + 4.333333333 -5t + t2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -5t + t2 = 4.333333333 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 4.333333333 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 4.333333333 + 6.25 Combine like terms: 4.333333333 + 6.25 = 10.583333333 6.25 + -5t + t2 = 10.583333333 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 10.583333333 Calculate the square root of the right side: 3.253203549 Break this problem into two subproblems by setting (t + -2.5) equal to 3.253203549 and -3.253203549.Subproblem 1
t + -2.5 = 3.253203549 Simplifying t + -2.5 = 3.253203549 Reorder the terms: -2.5 + t = 3.253203549 Solving -2.5 + t = 3.253203549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 3.253203549 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 3.253203549 + 2.5 t = 3.253203549 + 2.5 Combine like terms: 3.253203549 + 2.5 = 5.753203549 t = 5.753203549 Simplifying t = 5.753203549Subproblem 2
t + -2.5 = -3.253203549 Simplifying t + -2.5 = -3.253203549 Reorder the terms: -2.5 + t = -3.253203549 Solving -2.5 + t = -3.253203549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -3.253203549 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -3.253203549 + 2.5 t = -3.253203549 + 2.5 Combine like terms: -3.253203549 + 2.5 = -0.753203549 t = -0.753203549 Simplifying t = -0.753203549Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.753203549, -0.753203549}
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