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Simplifying 0 = -16t2 + 144t + 4 Reorder the terms: 0 = 4 + 144t + -16t2 Solving 0 = 4 + 144t + -16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -144t + 16t2 = 4 + 144t + -16t2 + -4 + -144t + 16t2 Reorder the terms: -4 + -144t + 16t2 = 4 + -4 + 144t + -144t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -144t + 16t2 = 0 + 144t + -144t + -16t2 + 16t2 -4 + -144t + 16t2 = 144t + -144t + -16t2 + 16t2 Combine like terms: 144t + -144t = 0 -4 + -144t + 16t2 = 0 + -16t2 + 16t2 -4 + -144t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -144t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -36t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -36t + 4t2)' equal to zero and attempt to solve: Simplifying -1 + -36t + 4t2 = 0 Solving -1 + -36t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -9t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -9t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -9t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -9t + t2 = 0 + 0.25 -9t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -9t + t2 = 0.25 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = 0.25 + 20.25 Reorder the terms: 20.25 + -9t + t2 = 0.25 + 20.25 Combine like terms: 0.25 + 20.25 = 20.5 20.25 + -9t + t2 = 20.5 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (t + -4.5) equal to 4.527692569 and -4.527692569.Subproblem 1
t + -4.5 = 4.527692569 Simplifying t + -4.5 = 4.527692569 Reorder the terms: -4.5 + t = 4.527692569 Solving -4.5 + t = 4.527692569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 4.527692569 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 4.527692569 + 4.5 t = 4.527692569 + 4.5 Combine like terms: 4.527692569 + 4.5 = 9.027692569 t = 9.027692569 Simplifying t = 9.027692569Subproblem 2
t + -4.5 = -4.527692569 Simplifying t + -4.5 = -4.527692569 Reorder the terms: -4.5 + t = -4.527692569 Solving -4.5 + t = -4.527692569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -4.527692569 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -4.527692569 + 4.5 t = -4.527692569 + 4.5 Combine like terms: -4.527692569 + 4.5 = -0.027692569 t = -0.027692569 Simplifying t = -0.027692569Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.027692569, -0.027692569}Solution
t = {9.027692569, -0.027692569}
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