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Simplifying t4 + -26t2 + 24 = 0 Reorder the terms: 24 + -26t2 + t4 = 0 Solving 24 + -26t2 + t4 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -26t2 + -24 + t4 = 0 + -24 Reorder the terms: 24 + -24 + -26t2 + t4 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -26t2 + t4 = 0 + -24 -26t2 + t4 = 0 + -24 Combine like terms: 0 + -24 = -24 -26t2 + t4 = -24 The t term is -26t2. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26t2 + 169 + t4 = -24 + 169 Reorder the terms: 169 + -26t2 + t4 = -24 + 169 Combine like terms: -24 + 169 = 145 169 + -26t2 + t4 = 145 Factor a perfect square on the left side: (t2 + -13)(t2 + -13) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (t2 + -13) equal to 12.041594579 and -12.041594579.Subproblem 1
t2 + -13 = 12.041594579 Simplifying t2 + -13 = 12.041594579 Reorder the terms: -13 + t2 = 12.041594579 Solving -13 + t2 = 12.041594579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t2 = 12.041594579 + 13 Combine like terms: -13 + 13 = 0 0 + t2 = 12.041594579 + 13 t2 = 12.041594579 + 13 Combine like terms: 12.041594579 + 13 = 25.041594579 t2 = 25.041594579 Simplifying t2 = 25.041594579 Take the square root of each side: t = {-5.004157729, 5.004157729}Subproblem 2
t2 + -13 = -12.041594579 Simplifying t2 + -13 = -12.041594579 Reorder the terms: -13 + t2 = -12.041594579 Solving -13 + t2 = -12.041594579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t2 = -12.041594579 + 13 Combine like terms: -13 + 13 = 0 0 + t2 = -12.041594579 + 13 t2 = -12.041594579 + 13 Combine like terms: -12.041594579 + 13 = 0.958405421 t2 = 0.958405421 Simplifying t2 = 0.958405421 Take the square root of each side: t = {-0.978981829, 0.978981829}Solution
The solution to the problem is based on the solutions from the subproblems. t = {-5.004157729, 5.004157729, -0.978981829, 0.978981829}
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