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Simplifying 16t2 + -20t + -60 = 0 Reorder the terms: -60 + -20t + 16t2 = 0 Solving -60 + -20t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -5t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -5t + 4t2)' equal to zero and attempt to solve: Simplifying -15 + -5t + 4t2 = 0 Solving -15 + -5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -1.25t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -1.25t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -1.25t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -1.25t + t2 = 0 + 3.75 -1.25t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -1.25t + t2 = 3.75 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = 3.75 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 3.75 + 0.390625 Combine like terms: 3.75 + 0.390625 = 4.140625 0.390625 + -1.25t + t2 = 4.140625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (t + -0.625) equal to 2.034852575 and -2.034852575.Subproblem 1
t + -0.625 = 2.034852575 Simplifying t + -0.625 = 2.034852575 Reorder the terms: -0.625 + t = 2.034852575 Solving -0.625 + t = 2.034852575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 2.034852575 + 0.625 t = 2.034852575 + 0.625 Combine like terms: 2.034852575 + 0.625 = 2.659852575 t = 2.659852575 Simplifying t = 2.659852575Subproblem 2
t + -0.625 = -2.034852575 Simplifying t + -0.625 = -2.034852575 Reorder the terms: -0.625 + t = -2.034852575 Solving -0.625 + t = -2.034852575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -2.034852575 + 0.625 t = -2.034852575 + 0.625 Combine like terms: -2.034852575 + 0.625 = -1.409852575 t = -1.409852575 Simplifying t = -1.409852575Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.659852575, -1.409852575}Solution
t = {2.659852575, -1.409852575}
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