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Simplifying -16t2 + 24t + 50 = 0 Reorder the terms: 50 + 24t + -16t2 = 0 Solving 50 + 24t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 12t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 12t + -8t2)' equal to zero and attempt to solve: Simplifying 25 + 12t + -8t2 = 0 Solving 25 + 12t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -1.5t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -1.5t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -1.5t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -1.5t + t2 = 0 + 3.125 -1.5t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -1.5t + t2 = 3.125 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 = 3.125 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = 3.125 + 0.5625 Combine like terms: 3.125 + 0.5625 = 3.6875 0.5625 + -1.5t + t2 = 3.6875 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = 3.6875 Calculate the square root of the right side: 1.920286437 Break this problem into two subproblems by setting (t + -0.75) equal to 1.920286437 and -1.920286437.Subproblem 1
t + -0.75 = 1.920286437 Simplifying t + -0.75 = 1.920286437 Reorder the terms: -0.75 + t = 1.920286437 Solving -0.75 + t = 1.920286437 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 = 1.920286437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 1.920286437 + 0.75 t = 1.920286437 + 0.75 Combine like terms: 1.920286437 + 0.75 = 2.670286437 t = 2.670286437 Simplifying t = 2.670286437Subproblem 2
t + -0.75 = -1.920286437 Simplifying t + -0.75 = -1.920286437 Reorder the terms: -0.75 + t = -1.920286437 Solving -0.75 + t = -1.920286437 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 = -1.920286437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -1.920286437 + 0.75 t = -1.920286437 + 0.75 Combine like terms: -1.920286437 + 0.75 = -1.170286437 t = -1.170286437 Simplifying t = -1.170286437Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.670286437, -1.170286437}Solution
t = {2.670286437, -1.170286437}
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