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Simplifying 27 = 47t + -5t2 Solving 27 = 47t + -5t2 Solving for variable 't'. Reorder the terms: 27 + -47t + 5t2 = 47t + -47t + -5t2 + 5t2 Combine like terms: 47t + -47t = 0 27 + -47t + 5t2 = 0 + -5t2 + 5t2 27 + -47t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 27 + -47t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.4 + -9.4t + t2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + -9.4t + -5.4 + t2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + -9.4t + t2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + -9.4t + t2 = 0 + -5.4 -9.4t + t2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 -9.4t + t2 = -5.4 The t term is -9.4t. Take half its coefficient (-4.7). Square it (22.09) and add it to both sides. Add '22.09' to each side of the equation. -9.4t + 22.09 + t2 = -5.4 + 22.09 Reorder the terms: 22.09 + -9.4t + t2 = -5.4 + 22.09 Combine like terms: -5.4 + 22.09 = 16.69 22.09 + -9.4t + t2 = 16.69 Factor a perfect square on the left side: (t + -4.7)(t + -4.7) = 16.69 Calculate the square root of the right side: 4.085339643 Break this problem into two subproblems by setting (t + -4.7) equal to 4.085339643 and -4.085339643.Subproblem 1
t + -4.7 = 4.085339643 Simplifying t + -4.7 = 4.085339643 Reorder the terms: -4.7 + t = 4.085339643 Solving -4.7 + t = 4.085339643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + t = 4.085339643 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + t = 4.085339643 + 4.7 t = 4.085339643 + 4.7 Combine like terms: 4.085339643 + 4.7 = 8.785339643 t = 8.785339643 Simplifying t = 8.785339643Subproblem 2
t + -4.7 = -4.085339643 Simplifying t + -4.7 = -4.085339643 Reorder the terms: -4.7 + t = -4.085339643 Solving -4.7 + t = -4.085339643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + t = -4.085339643 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + t = -4.085339643 + 4.7 t = -4.085339643 + 4.7 Combine like terms: -4.085339643 + 4.7 = 0.614660357 t = 0.614660357 Simplifying t = 0.614660357Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.785339643, 0.614660357}
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