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Simplifying -16t2 + 32t + 300 = 0 Reorder the terms: 300 + 32t + -16t2 = 0 Solving 300 + 32t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(75 + 8t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(75 + 8t + -4t2)' equal to zero and attempt to solve: Simplifying 75 + 8t + -4t2 = 0 Solving 75 + 8t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -18.75 + -2t + t2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -2t + 18.75 + t2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -2t + t2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -2t + t2 = 0 + 18.75 -2t + t2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -2t + t2 = 18.75 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 18.75 + 1 Reorder the terms: 1 + -2t + t2 = 18.75 + 1 Combine like terms: 18.75 + 1 = 19.75 1 + -2t + t2 = 19.75 Factor a perfect square on the left side: (t + -1)(t + -1) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (t + -1) equal to 4.444097209 and -4.444097209.Subproblem 1
t + -1 = 4.444097209 Simplifying t + -1 = 4.444097209 Reorder the terms: -1 + t = 4.444097209 Solving -1 + t = 4.444097209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 4.444097209 + 1 Combine like terms: -1 + 1 = 0 0 + t = 4.444097209 + 1 t = 4.444097209 + 1 Combine like terms: 4.444097209 + 1 = 5.444097209 t = 5.444097209 Simplifying t = 5.444097209Subproblem 2
t + -1 = -4.444097209 Simplifying t + -1 = -4.444097209 Reorder the terms: -1 + t = -4.444097209 Solving -1 + t = -4.444097209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -4.444097209 + 1 Combine like terms: -1 + 1 = 0 0 + t = -4.444097209 + 1 t = -4.444097209 + 1 Combine like terms: -4.444097209 + 1 = -3.444097209 t = -3.444097209 Simplifying t = -3.444097209Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.444097209, -3.444097209}Solution
t = {5.444097209, -3.444097209}
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