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Simplifying 7t4 + -10t2 + 1 = 0 Reorder the terms: 1 + -10t2 + 7t4 = 0 Solving 1 + -10t2 + 7t4 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -1.428571429t2 + t4 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -1.428571429t2 + -0.1428571429 + t4 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -1.428571429t2 + t4 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -1.428571429t2 + t4 = 0 + -0.1428571429 -1.428571429t2 + t4 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -1.428571429t2 + t4 = -0.1428571429 The t term is -1.428571429t2. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429t2 + 0.5102040819 + t4 = -0.1428571429 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429t2 + t4 = -0.1428571429 + 0.5102040819 Combine like terms: -0.1428571429 + 0.5102040819 = 0.367346939 0.5102040819 + -1.428571429t2 + t4 = 0.367346939 Factor a perfect square on the left side: (t2 + -0.7142857145)(t2 + -0.7142857145) = 0.367346939 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (t2 + -0.7142857145) equal to 0.606091527 and -0.606091527.Subproblem 1
t2 + -0.7142857145 = 0.606091527 Simplifying t2 + -0.7142857145 = 0.606091527 Reorder the terms: -0.7142857145 + t2 = 0.606091527 Solving -0.7142857145 + t2 = 0.606091527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t2 = 0.606091527 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t2 = 0.606091527 + 0.7142857145 t2 = 0.606091527 + 0.7142857145 Combine like terms: 0.606091527 + 0.7142857145 = 1.3203772415 t2 = 1.3203772415 Simplifying t2 = 1.3203772415 Take the square root of each side: t = {-1.149076691, 1.149076691}Subproblem 2
t2 + -0.7142857145 = -0.606091527 Simplifying t2 + -0.7142857145 = -0.606091527 Reorder the terms: -0.7142857145 + t2 = -0.606091527 Solving -0.7142857145 + t2 = -0.606091527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t2 = -0.606091527 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t2 = -0.606091527 + 0.7142857145 t2 = -0.606091527 + 0.7142857145 Combine like terms: -0.606091527 + 0.7142857145 = 0.1081941875 t2 = 0.1081941875 Simplifying t2 = 0.1081941875 Take the square root of each side: t = {-0.328928849, 0.328928849}Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.149076691, 1.149076691, -0.328928849, 0.328928849}
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