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Simplifying 220 = 16t2 + 128t Reorder the terms: 220 = 128t + 16t2 Solving 220 = 128t + 16t2 Solving for variable 't'. Reorder the terms: 220 + -128t + -16t2 = 128t + -128t + 16t2 + -16t2 Combine like terms: 128t + -128t = 0 220 + -128t + -16t2 = 0 + 16t2 + -16t2 220 + -128t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 220 + -128t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(55 + -32t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(55 + -32t + -4t2)' equal to zero and attempt to solve: Simplifying 55 + -32t + -4t2 = 0 Solving 55 + -32t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -13.75 + 8t + t2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 8t + 13.75 + t2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 8t + t2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 8t + t2 = 0 + 13.75 8t + t2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 8t + t2 = 13.75 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = 13.75 + 16 Reorder the terms: 16 + 8t + t2 = 13.75 + 16 Combine like terms: 13.75 + 16 = 29.75 16 + 8t + t2 = 29.75 Factor a perfect square on the left side: (t + 4)(t + 4) = 29.75 Calculate the square root of the right side: 5.454356057 Break this problem into two subproblems by setting (t + 4) equal to 5.454356057 and -5.454356057.Subproblem 1
t + 4 = 5.454356057 Simplifying t + 4 = 5.454356057 Reorder the terms: 4 + t = 5.454356057 Solving 4 + t = 5.454356057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 5.454356057 + -4 Combine like terms: 4 + -4 = 0 0 + t = 5.454356057 + -4 t = 5.454356057 + -4 Combine like terms: 5.454356057 + -4 = 1.454356057 t = 1.454356057 Simplifying t = 1.454356057Subproblem 2
t + 4 = -5.454356057 Simplifying t + 4 = -5.454356057 Reorder the terms: 4 + t = -5.454356057 Solving 4 + t = -5.454356057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -5.454356057 + -4 Combine like terms: 4 + -4 = 0 0 + t = -5.454356057 + -4 t = -5.454356057 + -4 Combine like terms: -5.454356057 + -4 = -9.454356057 t = -9.454356057 Simplifying t = -9.454356057Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.454356057, -9.454356057}Solution
t = {1.454356057, -9.454356057}
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