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Simplifying 144 + 80t + -16t2 = 0 Solving 144 + 80t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(9 + 5t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(9 + 5t + -1t2)' equal to zero and attempt to solve: Simplifying 9 + 5t + -1t2 = 0 Solving 9 + 5t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -5t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -5t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -5t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5t + t2 = 0 + 9 -5t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -5t + t2 = 9 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 9 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + -5t + t2 = 15.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (t + -2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
t + -2.5 = 3.905124838 Simplifying t + -2.5 = 3.905124838 Reorder the terms: -2.5 + t = 3.905124838 Solving -2.5 + t = 3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 3.905124838 + 2.5 t = 3.905124838 + 2.5 Combine like terms: 3.905124838 + 2.5 = 6.405124838 t = 6.405124838 Simplifying t = 6.405124838Subproblem 2
t + -2.5 = -3.905124838 Simplifying t + -2.5 = -3.905124838 Reorder the terms: -2.5 + t = -3.905124838 Solving -2.5 + t = -3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -3.905124838 + 2.5 t = -3.905124838 + 2.5 Combine like terms: -3.905124838 + 2.5 = -1.405124838 t = -1.405124838 Simplifying t = -1.405124838Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.405124838, -1.405124838}Solution
t = {6.405124838, -1.405124838}
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