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Simplifying 5t2 + -60t + -27 = 0 Reorder the terms: -27 + -60t + 5t2 = 0 Solving -27 + -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'. -5.4 + -12t + t2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -12t + 5.4 + t2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -12t + t2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -12t + t2 = 0 + 5.4 -12t + t2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -12t + t2 = 5.4 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 = 5.4 + 36 Reorder the terms: 36 + -12t + t2 = 5.4 + 36 Combine like terms: 5.4 + 36 = 41.4 36 + -12t + t2 = 41.4 Factor a perfect square on the left side: (t + -6)(t + -6) = 41.4 Calculate the square root of the right side: 6.434283177 Break this problem into two subproblems by setting (t + -6) equal to 6.434283177 and -6.434283177.Subproblem 1
t + -6 = 6.434283177 Simplifying t + -6 = 6.434283177 Reorder the terms: -6 + t = 6.434283177 Solving -6 + t = 6.434283177 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 = 6.434283177 + 6 Combine like terms: -6 + 6 = 0 0 + t = 6.434283177 + 6 t = 6.434283177 + 6 Combine like terms: 6.434283177 + 6 = 12.434283177 t = 12.434283177 Simplifying t = 12.434283177Subproblem 2
t + -6 = -6.434283177 Simplifying t + -6 = -6.434283177 Reorder the terms: -6 + t = -6.434283177 Solving -6 + t = -6.434283177 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 = -6.434283177 + 6 Combine like terms: -6 + 6 = 0 0 + t = -6.434283177 + 6 t = -6.434283177 + 6 Combine like terms: -6.434283177 + 6 = -0.434283177 t = -0.434283177 Simplifying t = -0.434283177Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.434283177, -0.434283177}
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