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Simplifying 5t2 + 7t + -8 = 0 Reorder the terms: -8 + 7t + 5t2 = 0 Solving -8 + 7t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 1.4t + t2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 1.4t + 1.6 + t2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 1.4t + t2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 1.4t + t2 = 0 + 1.6 1.4t + t2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 1.4t + t2 = 1.6 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 = 1.6 + 0.49 Reorder the terms: 0.49 + 1.4t + t2 = 1.6 + 0.49 Combine like terms: 1.6 + 0.49 = 2.09 0.49 + 1.4t + t2 = 2.09 Factor a perfect square on the left side: (t + 0.7)(t + 0.7) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (t + 0.7) equal to 1.445683229 and -1.445683229.Subproblem 1
t + 0.7 = 1.445683229 Simplifying t + 0.7 = 1.445683229 Reorder the terms: 0.7 + t = 1.445683229 Solving 0.7 + t = 1.445683229 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 = 1.445683229 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = 1.445683229 + -0.7 t = 1.445683229 + -0.7 Combine like terms: 1.445683229 + -0.7 = 0.745683229 t = 0.745683229 Simplifying t = 0.745683229Subproblem 2
t + 0.7 = -1.445683229 Simplifying t + 0.7 = -1.445683229 Reorder the terms: 0.7 + t = -1.445683229 Solving 0.7 + t = -1.445683229 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 = -1.445683229 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = -1.445683229 + -0.7 t = -1.445683229 + -0.7 Combine like terms: -1.445683229 + -0.7 = -2.145683229 t = -2.145683229 Simplifying t = -2.145683229Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.745683229, -2.145683229}
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