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Simplifying 47 = 73t + 5t2 Solving 47 = 73t + 5t2 Solving for variable 't'. Reorder the terms: 47 + -73t + -5t2 = 73t + -73t + 5t2 + -5t2 Combine like terms: 73t + -73t = 0 47 + -73t + -5t2 = 0 + 5t2 + -5t2 47 + -73t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 47 + -73t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -9.4 + 14.6t + t2 = 0 Move the constant term to the right: Add '9.4' to each side of the equation. -9.4 + 14.6t + 9.4 + t2 = 0 + 9.4 Reorder the terms: -9.4 + 9.4 + 14.6t + t2 = 0 + 9.4 Combine like terms: -9.4 + 9.4 = 0.0 0.0 + 14.6t + t2 = 0 + 9.4 14.6t + t2 = 0 + 9.4 Combine like terms: 0 + 9.4 = 9.4 14.6t + t2 = 9.4 The t term is 14.6t. Take half its coefficient (7.3). Square it (53.29) and add it to both sides. Add '53.29' to each side of the equation. 14.6t + 53.29 + t2 = 9.4 + 53.29 Reorder the terms: 53.29 + 14.6t + t2 = 9.4 + 53.29 Combine like terms: 9.4 + 53.29 = 62.69 53.29 + 14.6t + t2 = 62.69 Factor a perfect square on the left side: (t + 7.3)(t + 7.3) = 62.69 Calculate the square root of the right side: 7.917701687 Break this problem into two subproblems by setting (t + 7.3) equal to 7.917701687 and -7.917701687.Subproblem 1
t + 7.3 = 7.917701687 Simplifying t + 7.3 = 7.917701687 Reorder the terms: 7.3 + t = 7.917701687 Solving 7.3 + t = 7.917701687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.3' to each side of the equation. 7.3 + -7.3 + t = 7.917701687 + -7.3 Combine like terms: 7.3 + -7.3 = 0.0 0.0 + t = 7.917701687 + -7.3 t = 7.917701687 + -7.3 Combine like terms: 7.917701687 + -7.3 = 0.617701687 t = 0.617701687 Simplifying t = 0.617701687Subproblem 2
t + 7.3 = -7.917701687 Simplifying t + 7.3 = -7.917701687 Reorder the terms: 7.3 + t = -7.917701687 Solving 7.3 + t = -7.917701687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.3' to each side of the equation. 7.3 + -7.3 + t = -7.917701687 + -7.3 Combine like terms: 7.3 + -7.3 = 0.0 0.0 + t = -7.917701687 + -7.3 t = -7.917701687 + -7.3 Combine like terms: -7.917701687 + -7.3 = -15.217701687 t = -15.217701687 Simplifying t = -15.217701687Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.617701687, -15.217701687}
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