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Simplifying 156 + -8t + -16t2 = 0 Solving 156 + -8t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(39 + -2t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(39 + -2t + -4t2)' equal to zero and attempt to solve: Simplifying 39 + -2t + -4t2 = 0 Solving 39 + -2t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -9.75 + 0.5t + t2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + 0.5t + 9.75 + t2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + 0.5t + t2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + 0.5t + t2 = 0 + 9.75 0.5t + t2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 0.5t + t2 = 9.75 The t term is 0.5t. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5t + 0.0625 + t2 = 9.75 + 0.0625 Reorder the terms: 0.0625 + 0.5t + t2 = 9.75 + 0.0625 Combine like terms: 9.75 + 0.0625 = 9.8125 0.0625 + 0.5t + t2 = 9.8125 Factor a perfect square on the left side: (t + 0.25)(t + 0.25) = 9.8125 Calculate the square root of the right side: 3.132491022 Break this problem into two subproblems by setting (t + 0.25) equal to 3.132491022 and -3.132491022.Subproblem 1
t + 0.25 = 3.132491022 Simplifying t + 0.25 = 3.132491022 Reorder the terms: 0.25 + t = 3.132491022 Solving 0.25 + t = 3.132491022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = 3.132491022 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = 3.132491022 + -0.25 t = 3.132491022 + -0.25 Combine like terms: 3.132491022 + -0.25 = 2.882491022 t = 2.882491022 Simplifying t = 2.882491022Subproblem 2
t + 0.25 = -3.132491022 Simplifying t + 0.25 = -3.132491022 Reorder the terms: 0.25 + t = -3.132491022 Solving 0.25 + t = -3.132491022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = -3.132491022 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = -3.132491022 + -0.25 t = -3.132491022 + -0.25 Combine like terms: -3.132491022 + -0.25 = -3.382491022 t = -3.382491022 Simplifying t = -3.382491022Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.882491022, -3.382491022}Solution
t = {2.882491022, -3.382491022}
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