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Simplifying 60 = 2t2 + -6t + 7 Reorder the terms: 60 = 7 + -6t + 2t2 Solving 60 = 7 + -6t + 2t2 Solving for variable 't'. Combine like terms: 60 + -7 = 53 53 + 6t + -2t2 = 7 + -6t + 2t2 + -7 + 6t + -2t2 Reorder the terms: 53 + 6t + -2t2 = 7 + -7 + -6t + 6t + 2t2 + -2t2 Combine like terms: 7 + -7 = 0 53 + 6t + -2t2 = 0 + -6t + 6t + 2t2 + -2t2 53 + 6t + -2t2 = -6t + 6t + 2t2 + -2t2 Combine like terms: -6t + 6t = 0 53 + 6t + -2t2 = 0 + 2t2 + -2t2 53 + 6t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 53 + 6t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -26.5 + -3t + t2 = 0 Move the constant term to the right: Add '26.5' to each side of the equation. -26.5 + -3t + 26.5 + t2 = 0 + 26.5 Reorder the terms: -26.5 + 26.5 + -3t + t2 = 0 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + -3t + t2 = 0 + 26.5 -3t + t2 = 0 + 26.5 Combine like terms: 0 + 26.5 = 26.5 -3t + t2 = 26.5 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 = 26.5 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 26.5 + 2.25 Combine like terms: 26.5 + 2.25 = 28.75 2.25 + -3t + t2 = 28.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 28.75 Calculate the square root of the right side: 5.361902647 Break this problem into two subproblems by setting (t + -1.5) equal to 5.361902647 and -5.361902647.Subproblem 1
t + -1.5 = 5.361902647 Simplifying t + -1.5 = 5.361902647 Reorder the terms: -1.5 + t = 5.361902647 Solving -1.5 + t = 5.361902647 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 = 5.361902647 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 5.361902647 + 1.5 t = 5.361902647 + 1.5 Combine like terms: 5.361902647 + 1.5 = 6.861902647 t = 6.861902647 Simplifying t = 6.861902647Subproblem 2
t + -1.5 = -5.361902647 Simplifying t + -1.5 = -5.361902647 Reorder the terms: -1.5 + t = -5.361902647 Solving -1.5 + t = -5.361902647 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 = -5.361902647 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -5.361902647 + 1.5 t = -5.361902647 + 1.5 Combine like terms: -5.361902647 + 1.5 = -3.861902647 t = -3.861902647 Simplifying t = -3.861902647Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.861902647, -3.861902647}
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