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Simplifying 5t2 + -21t + -28 = 0 Reorder the terms: -28 + -21t + 5t2 = 0 Solving -28 + -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'. -5.6 + -4.2t + t2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -4.2t + 5.6 + t2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -4.2t + t2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -4.2t + t2 = 0 + 5.6 -4.2t + t2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -4.2t + t2 = 5.6 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 = 5.6 + 4.41 Reorder the terms: 4.41 + -4.2t + t2 = 5.6 + 4.41 Combine like terms: 5.6 + 4.41 = 10.01 4.41 + -4.2t + t2 = 10.01 Factor a perfect square on the left side: (t + -2.1)(t + -2.1) = 10.01 Calculate the square root of the right side: 3.163858404 Break this problem into two subproblems by setting (t + -2.1) equal to 3.163858404 and -3.163858404.Subproblem 1
t + -2.1 = 3.163858404 Simplifying t + -2.1 = 3.163858404 Reorder the terms: -2.1 + t = 3.163858404 Solving -2.1 + t = 3.163858404 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 = 3.163858404 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + t = 3.163858404 + 2.1 t = 3.163858404 + 2.1 Combine like terms: 3.163858404 + 2.1 = 5.263858404 t = 5.263858404 Simplifying t = 5.263858404Subproblem 2
t + -2.1 = -3.163858404 Simplifying t + -2.1 = -3.163858404 Reorder the terms: -2.1 + t = -3.163858404 Solving -2.1 + t = -3.163858404 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 = -3.163858404 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + t = -3.163858404 + 2.1 t = -3.163858404 + 2.1 Combine like terms: -3.163858404 + 2.1 = -1.063858404 t = -1.063858404 Simplifying t = -1.063858404Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.263858404, -1.063858404}
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