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Simplifying 12 + 2t + -0.25t2 = 0 Solving 12 + 2t + -0.25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -48 + -8t + t2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -8t + 48 + t2 = 0 + 48 Reorder the terms: -48 + 48 + -8t + t2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -8t + t2 = 0 + 48 -8t + t2 = 0 + 48 Combine like terms: 0 + 48 = 48 -8t + t2 = 48 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 48 + 16 Reorder the terms: 16 + -8t + t2 = 48 + 16 Combine like terms: 48 + 16 = 64 16 + -8t + t2 = 64 Factor a perfect square on the left side: (t + -4)(t + -4) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (t + -4) equal to 8 and -8.Subproblem 1
t + -4 = 8 Simplifying t + -4 = 8 Reorder the terms: -4 + t = 8 Solving -4 + t = 8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 8 + 4 Combine like terms: -4 + 4 = 0 0 + t = 8 + 4 t = 8 + 4 Combine like terms: 8 + 4 = 12 t = 12 Simplifying t = 12Subproblem 2
t + -4 = -8 Simplifying t + -4 = -8 Reorder the terms: -4 + t = -8 Solving -4 + t = -8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -8 + 4 Combine like terms: -4 + 4 = 0 0 + t = -8 + 4 t = -8 + 4 Combine like terms: -8 + 4 = -4 t = -4 Simplifying t = -4Solution
The solution to the problem is based on the solutions from the subproblems. t = {12, -4}
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