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Simplifying 5t2 + 7t = 9 Reorder the terms: 7t + 5t2 = 9 Solving 7t + 5t2 = 9 Solving for variable 't'. Reorder the terms: -9 + 7t + 5t2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 7t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 1.4t + t2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 1.4t + 1.8 + t2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 1.4t + t2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 1.4t + t2 = 0 + 1.8 1.4t + t2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 1.4t + t2 = 1.8 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 = 1.8 + 0.49 Reorder the terms: 0.49 + 1.4t + t2 = 1.8 + 0.49 Combine like terms: 1.8 + 0.49 = 2.29 0.49 + 1.4t + t2 = 2.29 Factor a perfect square on the left side: (t + 0.7)(t + 0.7) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (t + 0.7) equal to 1.513274595 and -1.513274595.Subproblem 1
t + 0.7 = 1.513274595 Simplifying t + 0.7 = 1.513274595 Reorder the terms: 0.7 + t = 1.513274595 Solving 0.7 + t = 1.513274595 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 = 1.513274595 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = 1.513274595 + -0.7 t = 1.513274595 + -0.7 Combine like terms: 1.513274595 + -0.7 = 0.813274595 t = 0.813274595 Simplifying t = 0.813274595Subproblem 2
t + 0.7 = -1.513274595 Simplifying t + 0.7 = -1.513274595 Reorder the terms: 0.7 + t = -1.513274595 Solving 0.7 + t = -1.513274595 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 = -1.513274595 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = -1.513274595 + -0.7 t = -1.513274595 + -0.7 Combine like terms: -1.513274595 + -0.7 = -2.213274595 t = -2.213274595 Simplifying t = -2.213274595Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.813274595, -2.213274595}
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