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Simplifying -16t2 + 64t + 144 = 0 Reorder the terms: 144 + 64t + -16t2 = 0 Solving 144 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(9 + 4t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(9 + 4t + -1t2)' equal to zero and attempt to solve: Simplifying 9 + 4t + -1t2 = 0 Solving 9 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -4t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -4t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -4t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4t + t2 = 0 + 9 -4t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4t + t2 = 9 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 9 + 4 Reorder the terms: 4 + -4t + t2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4t + t2 = 13 Factor a perfect square on the left side: (t + -2)(t + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (t + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
t + -2 = 3.605551275 Simplifying t + -2 = 3.605551275 Reorder the terms: -2 + t = 3.605551275 Solving -2 + t = 3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.605551275 + 2 t = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 t = 5.605551275 Simplifying t = 5.605551275Subproblem 2
t + -2 = -3.605551275 Simplifying t + -2 = -3.605551275 Reorder the terms: -2 + t = -3.605551275 Solving -2 + t = -3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.605551275 + 2 t = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 t = -1.605551275 Simplifying t = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.605551275, -1.605551275}Solution
t = {5.605551275, -1.605551275}
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