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Simplifying t4 + (4(t2)) + -225 = 0 Reorder the terms: -225 + (4t2) + t4 = 0 Solving -225 + (4t2) + t4 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + (4t2) + 225 + t4 = 0 + 225 Reorder the terms: -225 + 225 + (4t2) + t4 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + (4t2) + t4 = 0 + 225 (4t2) + t4 = 0 + 225 Combine like terms: 0 + 225 = 225 (4t2) + t4 = 225 The t term is (4t2). Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. (4t2) + 4 + t4 = 225 + 4 Reorder the terms: 4 + (4t2) + t4 = 225 + 4 Combine like terms: 225 + 4 = 229 4 + (4t2) + t4 = 229 Factor a perfect square on the left side: (t2 + 2)(t2 + 2) = 229 Calculate the square root of the right side: 15.13274595 Break this problem into two subproblems by setting (t2 + 2) equal to 15.13274595 and -15.13274595.Subproblem 1
t2 + 2 = 15.13274595 Simplifying t2 + 2 = 15.13274595 Reorder the terms: 2 + t2 = 15.13274595 Solving 2 + t2 = 15.13274595 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t2 = 15.13274595 + -2 Combine like terms: 2 + -2 = 0 0 + t2 = 15.13274595 + -2 t2 = 15.13274595 + -2 Combine like terms: 15.13274595 + -2 = 13.13274595 t2 = 13.13274595 Simplifying t2 = 13.13274595 Take the square root of each side: t = {-3.623913072, 3.623913072}Subproblem 2
t2 + 2 = -15.13274595 Simplifying t2 + 2 = -15.13274595 Reorder the terms: 2 + t2 = -15.13274595 Solving 2 + t2 = -15.13274595 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t2 = -15.13274595 + -2 Combine like terms: 2 + -2 = 0 0 + t2 = -15.13274595 + -2 t2 = -15.13274595 + -2 Combine like terms: -15.13274595 + -2 = -17.13274595 t2 = -17.13274595 Simplifying t2 = -17.13274595 Reorder the terms: 17.13274595 + t2 = -17.13274595 + 17.13274595 Combine like terms: -17.13274595 + 17.13274595 = 0.00000000 17.13274595 + 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.
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