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Simplifying 7t2 + 7t + -1 = 0 Reorder the terms: -1 + 7t + 7t2 = 0 Solving -1 + 7t + 7t2 = 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 + t + t2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + t + 0.1428571429 + t2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + t + t2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + t + t2 = 0 + 0.1428571429 t + t2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 t + t2 = 0.1428571429 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 0.1428571429 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 0.1428571429 + 0.25 Combine like terms: 0.1428571429 + 0.25 = 0.3928571429 1.25 + t2 = 0.3928571429 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.3928571429 Calculate the square root of the right side: 0.626783171 Break this problem into two subproblems by setting (t + 0.5) equal to 0.626783171 and -0.626783171.Subproblem 1
t + 0.5 = 0.626783171 Simplifying t + 0.5 = 0.626783171 Reorder the terms: 0.5 + t = 0.626783171 Solving 0.5 + t = 0.626783171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 0.626783171 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.626783171 + -0.5 t = 0.626783171 + -0.5 Combine like terms: 0.626783171 + -0.5 = 0.126783171 t = 0.126783171 Simplifying t = 0.126783171Subproblem 2
t + 0.5 = -0.626783171 Simplifying t + 0.5 = -0.626783171 Reorder the terms: 0.5 + t = -0.626783171 Solving 0.5 + t = -0.626783171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -0.626783171 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.626783171 + -0.5 t = -0.626783171 + -0.5 Combine like terms: -0.626783171 + -0.5 = -1.126783171 t = -1.126783171 Simplifying t = -1.126783171Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.126783171, -1.126783171}
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