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Simplifying -16t2 + 20t + 240 = 0 Reorder the terms: 240 + 20t + -16t2 = 0 Solving 240 + 20t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(60 + 5t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(60 + 5t + -4t2)' equal to zero and attempt to solve: Simplifying 60 + 5t + -4t2 = 0 Solving 60 + 5t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -15 + -1.25t + t2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -1.25t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + -1.25t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1.25t + t2 = 0 + 15 -1.25t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1.25t + t2 = 15 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 = 15 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 15 + 0.390625 Combine like terms: 15 + 0.390625 = 15.390625 0.390625 + -1.25t + t2 = 15.390625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 15.390625 Calculate the square root of the right side: 3.923088707 Break this problem into two subproblems by setting (t + -0.625) equal to 3.923088707 and -3.923088707.Subproblem 1
t + -0.625 = 3.923088707 Simplifying t + -0.625 = 3.923088707 Reorder the terms: -0.625 + t = 3.923088707 Solving -0.625 + t = 3.923088707 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 = 3.923088707 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 3.923088707 + 0.625 t = 3.923088707 + 0.625 Combine like terms: 3.923088707 + 0.625 = 4.548088707 t = 4.548088707 Simplifying t = 4.548088707Subproblem 2
t + -0.625 = -3.923088707 Simplifying t + -0.625 = -3.923088707 Reorder the terms: -0.625 + t = -3.923088707 Solving -0.625 + t = -3.923088707 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 = -3.923088707 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -3.923088707 + 0.625 t = -3.923088707 + 0.625 Combine like terms: -3.923088707 + 0.625 = -3.298088707 t = -3.298088707 Simplifying t = -3.298088707Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.548088707, -3.298088707}Solution
t = {4.548088707, -3.298088707}
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