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Simplifying -16t2 + 52t + 4 = 0 Reorder the terms: 4 + 52t + -16t2 = 0 Solving 4 + 52t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 13t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 13t + -4t2)' equal to zero and attempt to solve: Simplifying 1 + 13t + -4t2 = 0 Solving 1 + 13t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -3.25t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.25t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.25t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.25t + t2 = 0 + 0.25 -3.25t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.25t + t2 = 0.25 The t term is -3.25t. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25t + 2.640625 + t2 = 0.25 + 2.640625 Reorder the terms: 2.640625 + -3.25t + t2 = 0.25 + 2.640625 Combine like terms: 0.25 + 2.640625 = 2.890625 2.640625 + -3.25t + t2 = 2.890625 Factor a perfect square on the left side: (t + -1.625)(t + -1.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (t + -1.625) equal to 1.700183814 and -1.700183814.Subproblem 1
t + -1.625 = 1.700183814 Simplifying t + -1.625 = 1.700183814 Reorder the terms: -1.625 + t = 1.700183814 Solving -1.625 + t = 1.700183814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = 1.700183814 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = 1.700183814 + 1.625 t = 1.700183814 + 1.625 Combine like terms: 1.700183814 + 1.625 = 3.325183814 t = 3.325183814 Simplifying t = 3.325183814Subproblem 2
t + -1.625 = -1.700183814 Simplifying t + -1.625 = -1.700183814 Reorder the terms: -1.625 + t = -1.700183814 Solving -1.625 + t = -1.700183814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = -1.700183814 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = -1.700183814 + 1.625 t = -1.700183814 + 1.625 Combine like terms: -1.700183814 + 1.625 = -0.075183814 t = -0.075183814 Simplifying t = -0.075183814Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.325183814, -0.075183814}Solution
t = {3.325183814, -0.075183814}
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