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Simplifying 5t2 + -7t = 60 Reorder the terms: -7t + 5t2 = 60 Solving -7t + 5t2 = 60 Solving for variable 't'. Reorder the terms: -60 + -7t + 5t2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -7t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + -1.4t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.4t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -1.4t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.4t + t2 = 0 + 12 -1.4t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.4t + t2 = 12 The t term is -1.4t. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4t + 0.49 + t2 = 12 + 0.49 Reorder the terms: 0.49 + -1.4t + t2 = 12 + 0.49 Combine like terms: 12 + 0.49 = 12.49 0.49 + -1.4t + t2 = 12.49 Factor a perfect square on the left side: (t + -0.7)(t + -0.7) = 12.49 Calculate the square root of the right side: 3.534119409 Break this problem into two subproblems by setting (t + -0.7) equal to 3.534119409 and -3.534119409.Subproblem 1
t + -0.7 = 3.534119409 Simplifying t + -0.7 = 3.534119409 Reorder the terms: -0.7 + t = 3.534119409 Solving -0.7 + t = 3.534119409 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = 3.534119409 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 3.534119409 + 0.7 t = 3.534119409 + 0.7 Combine like terms: 3.534119409 + 0.7 = 4.234119409 t = 4.234119409 Simplifying t = 4.234119409Subproblem 2
t + -0.7 = -3.534119409 Simplifying t + -0.7 = -3.534119409 Reorder the terms: -0.7 + t = -3.534119409 Solving -0.7 + t = -3.534119409 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = -3.534119409 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -3.534119409 + 0.7 t = -3.534119409 + 0.7 Combine like terms: -3.534119409 + 0.7 = -2.834119409 t = -2.834119409 Simplifying t = -2.834119409Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.234119409, -2.834119409}
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