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Simplifying 10t2 + 15t + -40 = 0 Reorder the terms: -40 + 15t + 10t2 = 0 Solving -40 + 15t + 10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + 3t + 2t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-8 + 3t + 2t2)' equal to zero and attempt to solve: Simplifying -8 + 3t + 2t2 = 0 Solving -8 + 3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 1.5t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.5t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 1.5t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.5t + t2 = 0 + 4 1.5t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.5t + t2 = 4 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = 4 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + 1.5t + t2 = 4.5625 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (t + 0.75) equal to 2.136000936 and -2.136000936.Subproblem 1
t + 0.75 = 2.136000936 Simplifying t + 0.75 = 2.136000936 Reorder the terms: 0.75 + t = 2.136000936 Solving 0.75 + t = 2.136000936 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = 2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = 2.136000936 + -0.75 t = 2.136000936 + -0.75 Combine like terms: 2.136000936 + -0.75 = 1.386000936 t = 1.386000936 Simplifying t = 1.386000936Subproblem 2
t + 0.75 = -2.136000936 Simplifying t + 0.75 = -2.136000936 Reorder the terms: 0.75 + t = -2.136000936 Solving 0.75 + t = -2.136000936 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = -2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = -2.136000936 + -0.75 t = -2.136000936 + -0.75 Combine like terms: -2.136000936 + -0.75 = -2.886000936 t = -2.886000936 Simplifying t = -2.886000936Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.386000936, -2.886000936}Solution
t = {1.386000936, -2.886000936}
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