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Simplifying 4t2 + 10t + -16 = 0 Reorder the terms: -16 + 10t + 4t2 = 0 Solving -16 + 10t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 5t + 2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 5t + 2t2)' equal to zero and attempt to solve: Simplifying -8 + 5t + 2t2 = 0 Solving -8 + 5t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 2.5t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.5t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 2.5t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.5t + t2 = 0 + 4 2.5t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.5t + t2 = 4 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 4 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 4 + 1.5625 Combine like terms: 4 + 1.5625 = 5.5625 1.5625 + 2.5t + t2 = 5.5625 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (t + 1.25) equal to 2.358495283 and -2.358495283.Subproblem 1
t + 1.25 = 2.358495283 Simplifying t + 1.25 = 2.358495283 Reorder the terms: 1.25 + t = 2.358495283 Solving 1.25 + t = 2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 2.358495283 + -1.25 t = 2.358495283 + -1.25 Combine like terms: 2.358495283 + -1.25 = 1.108495283 t = 1.108495283 Simplifying t = 1.108495283Subproblem 2
t + 1.25 = -2.358495283 Simplifying t + 1.25 = -2.358495283 Reorder the terms: 1.25 + t = -2.358495283 Solving 1.25 + t = -2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -2.358495283 + -1.25 t = -2.358495283 + -1.25 Combine like terms: -2.358495283 + -1.25 = -3.608495283 t = -3.608495283 Simplifying t = -3.608495283Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.108495283, -3.608495283}Solution
t = {1.108495283, -3.608495283}
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