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Simplifying -2t2 + 24t + 4 = 0 Reorder the terms: 4 + 24t + -2t2 = 0 Solving 4 + 24t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 12t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 12t + -1t2)' equal to zero and attempt to solve: Simplifying 2 + 12t + -1t2 = 0 Solving 2 + 12t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -12t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -12t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -12t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -12t + t2 = 0 + 2 -12t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -12t + t2 = 2 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 2 + 36 Reorder the terms: 36 + -12t + t2 = 2 + 36 Combine like terms: 2 + 36 = 38 36 + -12t + t2 = 38 Factor a perfect square on the left side: (t + -6)(t + -6) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (t + -6) equal to 6.164414003 and -6.164414003.Subproblem 1
t + -6 = 6.164414003 Simplifying t + -6 = 6.164414003 Reorder the terms: -6 + t = 6.164414003 Solving -6 + t = 6.164414003 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + t = 6.164414003 + 6 t = 6.164414003 + 6 Combine like terms: 6.164414003 + 6 = 12.164414003 t = 12.164414003 Simplifying t = 12.164414003Subproblem 2
t + -6 = -6.164414003 Simplifying t + -6 = -6.164414003 Reorder the terms: -6 + t = -6.164414003 Solving -6 + t = -6.164414003 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + t = -6.164414003 + 6 t = -6.164414003 + 6 Combine like terms: -6.164414003 + 6 = -0.164414003 t = -0.164414003 Simplifying t = -0.164414003Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.164414003, -0.164414003}Solution
t = {12.164414003, -0.164414003}
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