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Simplifying 5t2 + 13t + -21 = 0 Reorder the terms: -21 + 13t + 5t2 = 0 Solving -21 + 13t + 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'. -4.2 + 2.6t + t2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 2.6t + 4.2 + t2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 2.6t + t2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 2.6t + t2 = 0 + 4.2 2.6t + t2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 2.6t + t2 = 4.2 The t term is 2.6t. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6t + 1.69 + t2 = 4.2 + 1.69 Reorder the terms: 1.69 + 2.6t + t2 = 4.2 + 1.69 Combine like terms: 4.2 + 1.69 = 5.89 1.69 + 2.6t + t2 = 5.89 Factor a perfect square on the left side: (t + 1.3)(t + 1.3) = 5.89 Calculate the square root of the right side: 2.42693222 Break this problem into two subproblems by setting (t + 1.3) equal to 2.42693222 and -2.42693222.Subproblem 1
t + 1.3 = 2.42693222 Simplifying t + 1.3 = 2.42693222 Reorder the terms: 1.3 + t = 2.42693222 Solving 1.3 + t = 2.42693222 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + t = 2.42693222 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + t = 2.42693222 + -1.3 t = 2.42693222 + -1.3 Combine like terms: 2.42693222 + -1.3 = 1.12693222 t = 1.12693222 Simplifying t = 1.12693222Subproblem 2
t + 1.3 = -2.42693222 Simplifying t + 1.3 = -2.42693222 Reorder the terms: 1.3 + t = -2.42693222 Solving 1.3 + t = -2.42693222 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + t = -2.42693222 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + t = -2.42693222 + -1.3 t = -2.42693222 + -1.3 Combine like terms: -2.42693222 + -1.3 = -3.72693222 t = -3.72693222 Simplifying t = -3.72693222Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.12693222, -3.72693222}
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