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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 = 43.89 53.29 + -14.6t + t2 = 43.89 Factor a perfect square on the left side: (t + -7.3)(t + -7.3) = 43.89 Calculate the square root of the right side: 6.62495283 Break this problem into two subproblems by setting (t + -7.3) equal to 6.62495283 and -6.62495283.Subproblem 1
t + -7.3 = 6.62495283 Simplifying t + -7.3 = 6.62495283 Reorder the terms: -7.3 + t = 6.62495283 Solving -7.3 + t = 6.62495283 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 = 6.62495283 + 7.3 Combine like terms: -7.3 + 7.3 = 0.0 0.0 + t = 6.62495283 + 7.3 t = 6.62495283 + 7.3 Combine like terms: 6.62495283 + 7.3 = 13.92495283 t = 13.92495283 Simplifying t = 13.92495283Subproblem 2
t + -7.3 = -6.62495283 Simplifying t + -7.3 = -6.62495283 Reorder the terms: -7.3 + t = -6.62495283 Solving -7.3 + t = -6.62495283 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 = -6.62495283 + 7.3 Combine like terms: -7.3 + 7.3 = 0.0 0.0 + t = -6.62495283 + 7.3 t = -6.62495283 + 7.3 Combine like terms: -6.62495283 + 7.3 = 0.67504717 t = 0.67504717 Simplifying t = 0.67504717Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.92495283, 0.67504717}
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