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Simplifying -16t2 + 64t + 224 = 0 Reorder the terms: 224 + 64t + -16t2 = 0 Solving 224 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(14 + 4t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(14 + 4t + -1t2)' equal to zero and attempt to solve: Simplifying 14 + 4t + -1t2 = 0 Solving 14 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -4t + t2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -4t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + -4t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -4t + t2 = 0 + 14 -4t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 -4t + t2 = 14 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 = 14 + 4 Reorder the terms: 4 + -4t + t2 = 14 + 4 Combine like terms: 14 + 4 = 18 4 + -4t + t2 = 18 Factor a perfect square on the left side: (t + -2)(t + -2) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (t + -2) equal to 4.242640687 and -4.242640687.Subproblem 1
t + -2 = 4.242640687 Simplifying t + -2 = 4.242640687 Reorder the terms: -2 + t = 4.242640687 Solving -2 + t = 4.242640687 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 = 4.242640687 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.242640687 + 2 t = 4.242640687 + 2 Combine like terms: 4.242640687 + 2 = 6.242640687 t = 6.242640687 Simplifying t = 6.242640687Subproblem 2
t + -2 = -4.242640687 Simplifying t + -2 = -4.242640687 Reorder the terms: -2 + t = -4.242640687 Solving -2 + t = -4.242640687 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 = -4.242640687 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.242640687 + 2 t = -4.242640687 + 2 Combine like terms: -4.242640687 + 2 = -2.242640687 t = -2.242640687 Simplifying t = -2.242640687Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.242640687, -2.242640687}Solution
t = {6.242640687, -2.242640687}
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