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Simplifying 5t2 + -21t + 14 = 0 Reorder the terms: 14 + -21t + 5t2 = 0 Solving 14 + -21t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + -4.2t + t2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + -4.2t + -2.8 + t2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + -4.2t + t2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + -4.2t + t2 = 0 + -2.8 -4.2t + t2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 -4.2t + t2 = -2.8 The t term is -4.2t. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2t + 4.41 + t2 = -2.8 + 4.41 Reorder the terms: 4.41 + -4.2t + t2 = -2.8 + 4.41 Combine like terms: -2.8 + 4.41 = 1.61 4.41 + -4.2t + t2 = 1.61 Factor a perfect square on the left side: (t + -2.1)(t + -2.1) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (t + -2.1) equal to 1.268857754 and -1.268857754.Subproblem 1
t + -2.1 = 1.268857754 Simplifying t + -2.1 = 1.268857754 Reorder the terms: -2.1 + t = 1.268857754 Solving -2.1 + t = 1.268857754 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + t = 1.268857754 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + t = 1.268857754 + 2.1 t = 1.268857754 + 2.1 Combine like terms: 1.268857754 + 2.1 = 3.368857754 t = 3.368857754 Simplifying t = 3.368857754Subproblem 2
t + -2.1 = -1.268857754 Simplifying t + -2.1 = -1.268857754 Reorder the terms: -2.1 + t = -1.268857754 Solving -2.1 + t = -1.268857754 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + t = -1.268857754 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + t = -1.268857754 + 2.1 t = -1.268857754 + 2.1 Combine like terms: -1.268857754 + 2.1 = 0.831142246 t = 0.831142246 Simplifying t = 0.831142246Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.368857754, 0.831142246}
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