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Simplifying 22t4 + 18t2 + -11t6 = 0 Reorder the terms: 18t2 + 22t4 + -11t6 = 0 Solving 18t2 + 22t4 + -11t6 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(18 + 22t2 + -11t4) = 0Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(18 + 22t2 + -11t4)' equal to zero and attempt to solve: Simplifying 18 + 22t2 + -11t4 = 0 Solving 18 + 22t2 + -11t4 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -1.636363636 + -2t2 + t4 = 0 Move the constant term to the right: Add '1.636363636' to each side of the equation. -1.636363636 + -2t2 + 1.636363636 + t4 = 0 + 1.636363636 Reorder the terms: -1.636363636 + 1.636363636 + -2t2 + t4 = 0 + 1.636363636 Combine like terms: -1.636363636 + 1.636363636 = 0.000000000 0.000000000 + -2t2 + t4 = 0 + 1.636363636 -2t2 + t4 = 0 + 1.636363636 Combine like terms: 0 + 1.636363636 = 1.636363636 -2t2 + t4 = 1.636363636 The t term is -2t2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t2 + 1 + t4 = 1.636363636 + 1 Reorder the terms: 1 + -2t2 + t4 = 1.636363636 + 1 Combine like terms: 1.636363636 + 1 = 2.636363636 1 + -2t2 + t4 = 2.636363636 Factor a perfect square on the left side: (t2 + -1)(t2 + -1) = 2.636363636 Calculate the square root of the right side: 1.623688282 Break this problem into two subproblems by setting (t2 + -1) equal to 1.623688282 and -1.623688282.Subproblem 1
t2 + -1 = 1.623688282 Simplifying t2 + -1 = 1.623688282 Reorder the terms: -1 + t2 = 1.623688282 Solving -1 + t2 = 1.623688282 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t2 = 1.623688282 + 1 Combine like terms: -1 + 1 = 0 0 + t2 = 1.623688282 + 1 t2 = 1.623688282 + 1 Combine like terms: 1.623688282 + 1 = 2.623688282 t2 = 2.623688282 Simplifying t2 = 2.623688282 Take the square root of each side: t = {-1.619780319, 1.619780319}Subproblem 2
t2 + -1 = -1.623688282 Simplifying t2 + -1 = -1.623688282 Reorder the terms: -1 + t2 = -1.623688282 Solving -1 + t2 = -1.623688282 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t2 = -1.623688282 + 1 Combine like terms: -1 + 1 = 0 0 + t2 = -1.623688282 + 1 t2 = -1.623688282 + 1 Combine like terms: -1.623688282 + 1 = -0.623688282 t2 = -0.623688282 Simplifying t2 = -0.623688282 Reorder the terms: 0.623688282 + t2 = -0.623688282 + 0.623688282 Combine like terms: -0.623688282 + 0.623688282 = 0.000000000 0.623688282 + t2 = 0.000000000 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.Solution
t = {0}
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