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Simplifying 5t2 + 47t = 27 Reorder the terms: 47t + 5t2 = 27 Solving 47t + 5t2 = 27 Solving for variable 't'. Reorder the terms: -27 + 47t + 5t2 = 27 + -27 Combine like terms: 27 + -27 = 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 = 27.49 22.09 + 9.4t + t2 = 27.49 Factor a perfect square on the left side: (t + 4.7)(t + 4.7) = 27.49 Calculate the square root of the right side: 5.243090692 Break this problem into two subproblems by setting (t + 4.7) equal to 5.243090692 and -5.243090692.Subproblem 1
t + 4.7 = 5.243090692 Simplifying t + 4.7 = 5.243090692 Reorder the terms: 4.7 + t = 5.243090692 Solving 4.7 + t = 5.243090692 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 = 5.243090692 + -4.7 Combine like terms: 4.7 + -4.7 = 0.0 0.0 + t = 5.243090692 + -4.7 t = 5.243090692 + -4.7 Combine like terms: 5.243090692 + -4.7 = 0.543090692 t = 0.543090692 Simplifying t = 0.543090692Subproblem 2
t + 4.7 = -5.243090692 Simplifying t + 4.7 = -5.243090692 Reorder the terms: 4.7 + t = -5.243090692 Solving 4.7 + t = -5.243090692 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 = -5.243090692 + -4.7 Combine like terms: 4.7 + -4.7 = 0.0 0.0 + t = -5.243090692 + -4.7 t = -5.243090692 + -4.7 Combine like terms: -5.243090692 + -4.7 = -9.943090692 t = -9.943090692 Simplifying t = -9.943090692Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.543090692, -9.943090692}
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