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Simplifying 2t2 + 5t + -10 = 0 Reorder the terms: -10 + 5t + 2t2 = 0 Solving -10 + 5t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 2.5t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.5t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + 2.5t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.5t + t2 = 0 + 5 2.5t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.5t + t2 = 5 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 5 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 5 + 1.5625 Combine like terms: 5 + 1.5625 = 6.5625 1.5625 + 2.5t + t2 = 6.5625 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (t + 1.25) equal to 2.561737691 and -2.561737691.Subproblem 1
t + 1.25 = 2.561737691 Simplifying t + 1.25 = 2.561737691 Reorder the terms: 1.25 + t = 2.561737691 Solving 1.25 + t = 2.561737691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 2.561737691 + -1.25 t = 2.561737691 + -1.25 Combine like terms: 2.561737691 + -1.25 = 1.311737691 t = 1.311737691 Simplifying t = 1.311737691Subproblem 2
t + 1.25 = -2.561737691 Simplifying t + 1.25 = -2.561737691 Reorder the terms: 1.25 + t = -2.561737691 Solving 1.25 + t = -2.561737691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -2.561737691 + -1.25 t = -2.561737691 + -1.25 Combine like terms: -2.561737691 + -1.25 = -3.811737691 t = -3.811737691 Simplifying t = -3.811737691Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.311737691, -3.811737691}
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