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Simplifying 300t = 300 + -32t2 Solving 300t = 300 + -32t2 Solving for variable 't'. Reorder the terms: -300 + 300t + 32t2 = 300 + -32t2 + -300 + 32t2 Reorder the terms: -300 + 300t + 32t2 = 300 + -300 + -32t2 + 32t2 Combine like terms: 300 + -300 = 0 -300 + 300t + 32t2 = 0 + -32t2 + 32t2 -300 + 300t + 32t2 = -32t2 + 32t2 Combine like terms: -32t2 + 32t2 = 0 -300 + 300t + 32t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-75 + 75t + 8t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-75 + 75t + 8t2)' equal to zero and attempt to solve: Simplifying -75 + 75t + 8t2 = 0 Solving -75 + 75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9.375 + 9.375t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 9.375t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 9.375t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 9.375t + t2 = 0 + 9.375 9.375t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 9.375t + t2 = 9.375 The t term is 9.375t. Take half its coefficient (4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. 9.375t + 21.97265625 + t2 = 9.375 + 21.97265625 Reorder the terms: 21.97265625 + 9.375t + t2 = 9.375 + 21.97265625 Combine like terms: 9.375 + 21.97265625 = 31.34765625 21.97265625 + 9.375t + t2 = 31.34765625 Factor a perfect square on the left side: (t + 4.6875)(t + 4.6875) = 31.34765625 Calculate the square root of the right side: 5.598897771 Break this problem into two subproblems by setting (t + 4.6875) equal to 5.598897771 and -5.598897771.Subproblem 1
t + 4.6875 = 5.598897771 Simplifying t + 4.6875 = 5.598897771 Reorder the terms: 4.6875 + t = 5.598897771 Solving 4.6875 + t = 5.598897771 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + t = 5.598897771 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = 5.598897771 + -4.6875 t = 5.598897771 + -4.6875 Combine like terms: 5.598897771 + -4.6875 = 0.911397771 t = 0.911397771 Simplifying t = 0.911397771Subproblem 2
t + 4.6875 = -5.598897771 Simplifying t + 4.6875 = -5.598897771 Reorder the terms: 4.6875 + t = -5.598897771 Solving 4.6875 + t = -5.598897771 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + t = -5.598897771 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = -5.598897771 + -4.6875 t = -5.598897771 + -4.6875 Combine like terms: -5.598897771 + -4.6875 = -10.286397771 t = -10.286397771 Simplifying t = -10.286397771Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.911397771, -10.286397771}Solution
t = {0.911397771, -10.286397771}
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