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Simplifying -16t4 + 88t2 + 80 = 0 Reorder the terms: 80 + 88t2 + -16t4 = 0 Solving 80 + 88t2 + -16t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(10 + 11t2 + -2t4) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(10 + 11t2 + -2t4)' equal to zero and attempt to solve: Simplifying 10 + 11t2 + -2t4 = 0 Solving 10 + 11t2 + -2t4 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5 + -5.5t2 + t4 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -5.5t2 + 5 + t4 = 0 + 5 Reorder the terms: -5 + 5 + -5.5t2 + t4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5.5t2 + t4 = 0 + 5 -5.5t2 + t4 = 0 + 5 Combine like terms: 0 + 5 = 5 -5.5t2 + t4 = 5 The t term is -5.5t2. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t2 + 7.5625 + t4 = 5 + 7.5625 Reorder the terms: 7.5625 + -5.5t2 + t4 = 5 + 7.5625 Combine like terms: 5 + 7.5625 = 12.5625 7.5625 + -5.5t2 + t4 = 12.5625 Factor a perfect square on the left side: (t2 + -2.75)(t2 + -2.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (t2 + -2.75) equal to 3.54436172 and -3.54436172.Subproblem 1
t2 + -2.75 = 3.54436172 Simplifying t2 + -2.75 = 3.54436172 Reorder the terms: -2.75 + t2 = 3.54436172 Solving -2.75 + t2 = 3.54436172 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t2 = 3.54436172 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t2 = 3.54436172 + 2.75 t2 = 3.54436172 + 2.75 Combine like terms: 3.54436172 + 2.75 = 6.29436172 t2 = 6.29436172 Simplifying t2 = 6.29436172 Take the square root of each side: t = {-2.508856656, 2.508856656}Subproblem 2
t2 + -2.75 = -3.54436172 Simplifying t2 + -2.75 = -3.54436172 Reorder the terms: -2.75 + t2 = -3.54436172 Solving -2.75 + t2 = -3.54436172 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t2 = -3.54436172 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t2 = -3.54436172 + 2.75 t2 = -3.54436172 + 2.75 Combine like terms: -3.54436172 + 2.75 = -0.79436172 t2 = -0.79436172 Simplifying t2 = -0.79436172 Reorder the terms: 0.79436172 + t2 = -0.79436172 + 0.79436172 Combine like terms: -0.79436172 + 0.79436172 = 0.00000000 0.79436172 + t2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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