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Simplifying 0 = 10t2 + 25t + -30 Reorder the terms: 0 = -30 + 25t + 10t2 Solving 0 = -30 + 25t + 10t2 Solving for variable 't'. Combine like terms: 0 + 30 = 30 30 + -25t + -10t2 = -30 + 25t + 10t2 + 30 + -25t + -10t2 Reorder the terms: 30 + -25t + -10t2 = -30 + 30 + 25t + -25t + 10t2 + -10t2 Combine like terms: -30 + 30 = 0 30 + -25t + -10t2 = 0 + 25t + -25t + 10t2 + -10t2 30 + -25t + -10t2 = 25t + -25t + 10t2 + -10t2 Combine like terms: 25t + -25t = 0 30 + -25t + -10t2 = 0 + 10t2 + -10t2 30 + -25t + -10t2 = 10t2 + -10t2 Combine like terms: 10t2 + -10t2 = 0 30 + -25t + -10t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -5t + -2t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -5t + -2t2)' equal to zero and attempt to solve: Simplifying 6 + -5t + -2t2 = 0 Solving 6 + -5t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3 + 2.5t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.5t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 2.5t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.5t + t2 = 0 + 3 2.5t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.5t + t2 = 3 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 = 3 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + 2.5t + t2 = 4.5625 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (t + 1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
t + 1.25 = 2.136000936 Simplifying t + 1.25 = 2.136000936 Reorder the terms: 1.25 + t = 2.136000936 Solving 1.25 + t = 2.136000936 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 = 2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 2.136000936 + -1.25 t = 2.136000936 + -1.25 Combine like terms: 2.136000936 + -1.25 = 0.886000936 t = 0.886000936 Simplifying t = 0.886000936Subproblem 2
t + 1.25 = -2.136000936 Simplifying t + 1.25 = -2.136000936 Reorder the terms: 1.25 + t = -2.136000936 Solving 1.25 + t = -2.136000936 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 = -2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -2.136000936 + -1.25 t = -2.136000936 + -1.25 Combine like terms: -2.136000936 + -1.25 = -3.386000936 t = -3.386000936 Simplifying t = -3.386000936Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.886000936, -3.386000936}Solution
t = {0.886000936, -3.386000936}
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