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Simplifying 4 = -3t2 + 15t + 8 Reorder the terms: 4 = 8 + 15t + -3t2 Solving 4 = 8 + 15t + -3t2 Solving for variable 't'. Combine like terms: 4 + -8 = -4 -4 + -15t + 3t2 = 8 + 15t + -3t2 + -8 + -15t + 3t2 Reorder the terms: -4 + -15t + 3t2 = 8 + -8 + 15t + -15t + -3t2 + 3t2 Combine like terms: 8 + -8 = 0 -4 + -15t + 3t2 = 0 + 15t + -15t + -3t2 + 3t2 -4 + -15t + 3t2 = 15t + -15t + -3t2 + 3t2 Combine like terms: 15t + -15t = 0 -4 + -15t + 3t2 = 0 + -3t2 + 3t2 -4 + -15t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 -4 + -15t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -5t + t2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -5t + 1.333333333 + t2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -5t + t2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -5t + t2 = 0 + 1.333333333 -5t + t2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -5t + t2 = 1.333333333 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 1.333333333 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 1.333333333 + 6.25 Combine like terms: 1.333333333 + 6.25 = 7.583333333 6.25 + -5t + t2 = 7.583333333 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 7.583333333 Calculate the square root of the right side: 2.753785274 Break this problem into two subproblems by setting (t + -2.5) equal to 2.753785274 and -2.753785274.Subproblem 1
t + -2.5 = 2.753785274 Simplifying t + -2.5 = 2.753785274 Reorder the terms: -2.5 + t = 2.753785274 Solving -2.5 + t = 2.753785274 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.753785274 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.753785274 + 2.5 t = 2.753785274 + 2.5 Combine like terms: 2.753785274 + 2.5 = 5.253785274 t = 5.253785274 Simplifying t = 5.253785274Subproblem 2
t + -2.5 = -2.753785274 Simplifying t + -2.5 = -2.753785274 Reorder the terms: -2.5 + t = -2.753785274 Solving -2.5 + t = -2.753785274 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.753785274 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.753785274 + 2.5 t = -2.753785274 + 2.5 Combine like terms: -2.753785274 + 2.5 = -0.253785274 t = -0.253785274 Simplifying t = -0.253785274Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.253785274, -0.253785274}
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