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Simplifying 5t2 + 33t + -40 = 0 Reorder the terms: -40 + 33t + 5t2 = 0 Solving -40 + 33t + 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'. -8 + 6.6t + t2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 6.6t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 6.6t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6.6t + t2 = 0 + 8 6.6t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 6.6t + t2 = 8 The t term is 6.6t. Take half its coefficient (3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. 6.6t + 10.89 + t2 = 8 + 10.89 Reorder the terms: 10.89 + 6.6t + t2 = 8 + 10.89 Combine like terms: 8 + 10.89 = 18.89 10.89 + 6.6t + t2 = 18.89 Factor a perfect square on the left side: (t + 3.3)(t + 3.3) = 18.89 Calculate the square root of the right side: 4.346262762 Break this problem into two subproblems by setting (t + 3.3) equal to 4.346262762 and -4.346262762.Subproblem 1
t + 3.3 = 4.346262762 Simplifying t + 3.3 = 4.346262762 Reorder the terms: 3.3 + t = 4.346262762 Solving 3.3 + t = 4.346262762 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + t = 4.346262762 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + t = 4.346262762 + -3.3 t = 4.346262762 + -3.3 Combine like terms: 4.346262762 + -3.3 = 1.046262762 t = 1.046262762 Simplifying t = 1.046262762Subproblem 2
t + 3.3 = -4.346262762 Simplifying t + 3.3 = -4.346262762 Reorder the terms: 3.3 + t = -4.346262762 Solving 3.3 + t = -4.346262762 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + t = -4.346262762 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + t = -4.346262762 + -3.3 t = -4.346262762 + -3.3 Combine like terms: -4.346262762 + -3.3 = -7.646262762 t = -7.646262762 Simplifying t = -7.646262762Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.046262762, -7.646262762}
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