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Simplifying -16t2 + 72t + 8 = 0 Reorder the terms: 8 + 72t + -16t2 = 0 Solving 8 + 72t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(1 + 9t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + 9t + -2t2)' equal to zero and attempt to solve: Simplifying 1 + 9t + -2t2 = 0 Solving 1 + 9t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -4.5t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4.5t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4.5t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4.5t + t2 = 0 + 0.5 -4.5t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4.5t + t2 = 0.5 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 0.5 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 0.5 + 5.0625 Combine like terms: 0.5 + 5.0625 = 5.5625 5.0625 + -4.5t + t2 = 5.5625 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (t + -2.25) equal to 2.358495283 and -2.358495283.Subproblem 1
t + -2.25 = 2.358495283 Simplifying t + -2.25 = 2.358495283 Reorder the terms: -2.25 + t = 2.358495283 Solving -2.25 + t = 2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 2.358495283 + 2.25 t = 2.358495283 + 2.25 Combine like terms: 2.358495283 + 2.25 = 4.608495283 t = 4.608495283 Simplifying t = 4.608495283Subproblem 2
t + -2.25 = -2.358495283 Simplifying t + -2.25 = -2.358495283 Reorder the terms: -2.25 + t = -2.358495283 Solving -2.25 + t = -2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -2.358495283 + 2.25 t = -2.358495283 + 2.25 Combine like terms: -2.358495283 + 2.25 = -0.108495283 t = -0.108495283 Simplifying t = -0.108495283Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.608495283, -0.108495283}Solution
t = {4.608495283, -0.108495283}
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