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Simplifying 24t + 24 = 1.5t2 Reorder the terms: 24 + 24t = 1.5t2 Solving 24 + 24t = 1.5t2 Solving for variable 't'. Combine like terms: 1.5t2 + -1.5t2 = 0.0 24 + 24t + -1.5t2 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -16 + -16t + t2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -16t + 16 + t2 = 0 + 16 Reorder the terms: -16 + 16 + -16t + t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -16t + t2 = 0 + 16 -16t + t2 = 0 + 16 Combine like terms: 0 + 16 = 16 -16t + t2 = 16 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = 16 + 64 Reorder the terms: 64 + -16t + t2 = 16 + 64 Combine like terms: 16 + 64 = 80 64 + -16t + t2 = 80 Factor a perfect square on the left side: (t + -8)(t + -8) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (t + -8) equal to 8.94427191 and -8.94427191.Subproblem 1
t + -8 = 8.94427191 Simplifying t + -8 = 8.94427191 Reorder the terms: -8 + t = 8.94427191 Solving -8 + t = 8.94427191 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 8.94427191 + 8 Combine like terms: -8 + 8 = 0 0 + t = 8.94427191 + 8 t = 8.94427191 + 8 Combine like terms: 8.94427191 + 8 = 16.94427191 t = 16.94427191 Simplifying t = 16.94427191Subproblem 2
t + -8 = -8.94427191 Simplifying t + -8 = -8.94427191 Reorder the terms: -8 + t = -8.94427191 Solving -8 + t = -8.94427191 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -8.94427191 + 8 Combine like terms: -8 + 8 = 0 0 + t = -8.94427191 + 8 t = -8.94427191 + 8 Combine like terms: -8.94427191 + 8 = -0.94427191 t = -0.94427191 Simplifying t = -0.94427191Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.94427191, -0.94427191}
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