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Simplifying (4t2) + 12t + -17 = 0 Reorder the terms: -17 + 12t + (4t2) = 0 Solving -17 + 12t + (4t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + 3t + t2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 3t + 4.25 + t2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 3t + t2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 3t + t2 = 0 + 4.25 3t + t2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 3t + t2 = 4.25 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = 4.25 + 2.25 Reorder the terms: 2.25 + 3t + t2 = 4.25 + 2.25 Combine like terms: 4.25 + 2.25 = 6.5 2.25 + 3t + t2 = 6.5 Factor a perfect square on the left side: ((t) + 1.5)((t) + 1.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting ((t) + 1.5) equal to 2.549509757 and -2.549509757.Subproblem 1
(t) + 1.5 = 2.549509757 Simplifying (t) + 1.5 = 2.549509757 t + 1.5 = 2.549509757 Reorder the terms: 1.5 + t = 2.549509757 Solving 1.5 + t = 2.549509757 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 2.549509757 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 2.549509757 + -1.5 t = 2.549509757 + -1.5 Combine like terms: 2.549509757 + -1.5 = 1.049509757 t = 1.049509757 Simplifying t = 1.049509757Subproblem 2
(t) + 1.5 = -2.549509757 Simplifying (t) + 1.5 = -2.549509757 t + 1.5 = -2.549509757 Reorder the terms: 1.5 + t = -2.549509757 Solving 1.5 + t = -2.549509757 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -2.549509757 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -2.549509757 + -1.5 t = -2.549509757 + -1.5 Combine like terms: -2.549509757 + -1.5 = -4.049509757 t = -4.049509757 Simplifying t = -4.049509757Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.049509757, -4.049509757}
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