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Simplifying (5t2) + 32t + -160 = 0 Reorder the terms: -160 + 32t + (5t2) = 0 Solving -160 + 32t + (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'. -32 + 6.4t + t2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 6.4t + 32 + t2 = 0 + 32 Reorder the terms: -32 + 32 + 6.4t + t2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 6.4t + t2 = 0 + 32 6.4t + t2 = 0 + 32 Combine like terms: 0 + 32 = 32 6.4t + t2 = 32 The t term is 6.4t. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4t + 10.24 + t2 = 32 + 10.24 Reorder the terms: 10.24 + 6.4t + t2 = 32 + 10.24 Combine like terms: 32 + 10.24 = 42.24 10.24 + 6.4t + t2 = 42.24 Factor a perfect square on the left side: ((t) + 3.2)((t) + 3.2) = 42.24 Calculate the square root of the right side: 6.499230724 Break this problem into two subproblems by setting ((t) + 3.2) equal to 6.499230724 and -6.499230724.Subproblem 1
(t) + 3.2 = 6.499230724 Simplifying (t) + 3.2 = 6.499230724 t + 3.2 = 6.499230724 Reorder the terms: 3.2 + t = 6.499230724 Solving 3.2 + t = 6.499230724 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + t = 6.499230724 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + t = 6.499230724 + -3.2 t = 6.499230724 + -3.2 Combine like terms: 6.499230724 + -3.2 = 3.299230724 t = 3.299230724 Simplifying t = 3.299230724Subproblem 2
(t) + 3.2 = -6.499230724 Simplifying (t) + 3.2 = -6.499230724 t + 3.2 = -6.499230724 Reorder the terms: 3.2 + t = -6.499230724 Solving 3.2 + t = -6.499230724 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + t = -6.499230724 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + t = -6.499230724 + -3.2 t = -6.499230724 + -3.2 Combine like terms: -6.499230724 + -3.2 = -9.699230724 t = -9.699230724 Simplifying t = -9.699230724Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.299230724, -9.699230724}
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