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Simplifying -5t2 + 60t + 74 = 0 Reorder the terms: 74 + 60t + -5t2 = 0 Solving 74 + 60t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -14.8 + -12t + t2 = 0 Move the constant term to the right: Add '14.8' to each side of the equation. -14.8 + -12t + 14.8 + t2 = 0 + 14.8 Reorder the terms: -14.8 + 14.8 + -12t + t2 = 0 + 14.8 Combine like terms: -14.8 + 14.8 = 0.0 0.0 + -12t + t2 = 0 + 14.8 -12t + t2 = 0 + 14.8 Combine like terms: 0 + 14.8 = 14.8 -12t + t2 = 14.8 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 14.8 + 36 Reorder the terms: 36 + -12t + t2 = 14.8 + 36 Combine like terms: 14.8 + 36 = 50.8 36 + -12t + t2 = 50.8 Factor a perfect square on the left side: (t + -6)(t + -6) = 50.8 Calculate the square root of the right side: 7.127411872 Break this problem into two subproblems by setting (t + -6) equal to 7.127411872 and -7.127411872.Subproblem 1
t + -6 = 7.127411872 Simplifying t + -6 = 7.127411872 Reorder the terms: -6 + t = 7.127411872 Solving -6 + t = 7.127411872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 7.127411872 + 6 Combine like terms: -6 + 6 = 0 0 + t = 7.127411872 + 6 t = 7.127411872 + 6 Combine like terms: 7.127411872 + 6 = 13.127411872 t = 13.127411872 Simplifying t = 13.127411872Subproblem 2
t + -6 = -7.127411872 Simplifying t + -6 = -7.127411872 Reorder the terms: -6 + t = -7.127411872 Solving -6 + t = -7.127411872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -7.127411872 + 6 Combine like terms: -6 + 6 = 0 0 + t = -7.127411872 + 6 t = -7.127411872 + 6 Combine like terms: -7.127411872 + 6 = -1.127411872 t = -1.127411872 Simplifying t = -1.127411872Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.127411872, -1.127411872}
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