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Simplifying 7t2 + 4t = 5 Reorder the terms: 4t + 7t2 = 5 Solving 4t + 7t2 = 5 Solving for variable 't'. Reorder the terms: -5 + 4t + 7t2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 4t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 0.5714285714t + t2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.5714285714t + 0.7142857143 + t2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.5714285714t + t2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.5714285714t + t2 = 0 + 0.7142857143 0.5714285714t + t2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.5714285714t + t2 = 0.7142857143 The t term is 0.5714285714t. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714t + 0.08163265305 + t2 = 0.7142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714t + t2 = 0.7142857143 + 0.08163265305 Combine like terms: 0.7142857143 + 0.08163265305 = 0.79591836735 0.08163265305 + 0.5714285714t + t2 = 0.79591836735 Factor a perfect square on the left side: (t + 0.2857142857)(t + 0.2857142857) = 0.79591836735 Calculate the square root of the right side: 0.892142571 Break this problem into two subproblems by setting (t + 0.2857142857) equal to 0.892142571 and -0.892142571.Subproblem 1
t + 0.2857142857 = 0.892142571 Simplifying t + 0.2857142857 = 0.892142571 Reorder the terms: 0.2857142857 + t = 0.892142571 Solving 0.2857142857 + t = 0.892142571 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + t = 0.892142571 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + t = 0.892142571 + -0.2857142857 t = 0.892142571 + -0.2857142857 Combine like terms: 0.892142571 + -0.2857142857 = 0.6064282853 t = 0.6064282853 Simplifying t = 0.6064282853Subproblem 2
t + 0.2857142857 = -0.892142571 Simplifying t + 0.2857142857 = -0.892142571 Reorder the terms: 0.2857142857 + t = -0.892142571 Solving 0.2857142857 + t = -0.892142571 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + t = -0.892142571 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + t = -0.892142571 + -0.2857142857 t = -0.892142571 + -0.2857142857 Combine like terms: -0.892142571 + -0.2857142857 = -1.1778568567 t = -1.1778568567 Simplifying t = -1.1778568567Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6064282853, -1.1778568567}
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