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Simplifying 10t2 + 16t + -9 = 0 Reorder the terms: -9 + 16t + 10t2 = 0 Solving -9 + 16t + 10t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 1.6t + t2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 1.6t + 0.9 + t2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 1.6t + t2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 1.6t + t2 = 0 + 0.9 1.6t + t2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 1.6t + t2 = 0.9 The t term is 1.6t. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6t + 0.64 + t2 = 0.9 + 0.64 Reorder the terms: 0.64 + 1.6t + t2 = 0.9 + 0.64 Combine like terms: 0.9 + 0.64 = 1.54 0.64 + 1.6t + t2 = 1.54 Factor a perfect square on the left side: (t + 0.8)(t + 0.8) = 1.54 Calculate the square root of the right side: 1.240967365 Break this problem into two subproblems by setting (t + 0.8) equal to 1.240967365 and -1.240967365.Subproblem 1
t + 0.8 = 1.240967365 Simplifying t + 0.8 = 1.240967365 Reorder the terms: 0.8 + t = 1.240967365 Solving 0.8 + t = 1.240967365 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = 1.240967365 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = 1.240967365 + -0.8 t = 1.240967365 + -0.8 Combine like terms: 1.240967365 + -0.8 = 0.440967365 t = 0.440967365 Simplifying t = 0.440967365Subproblem 2
t + 0.8 = -1.240967365 Simplifying t + 0.8 = -1.240967365 Reorder the terms: 0.8 + t = -1.240967365 Solving 0.8 + t = -1.240967365 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = -1.240967365 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = -1.240967365 + -0.8 t = -1.240967365 + -0.8 Combine like terms: -1.240967365 + -0.8 = -2.040967365 t = -2.040967365 Simplifying t = -2.040967365Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.440967365, -2.040967365}
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