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Simplifying -4t2 + -15t = -14 Reorder the terms: -15t + -4t2 = -14 Solving -15t + -4t2 = -14 Solving for variable 't'. Reorder the terms: 14 + -15t + -4t2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + -15t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.5 + 3.75t + t2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3.75t + 3.5 + t2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3.75t + t2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3.75t + t2 = 0 + 3.5 3.75t + t2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3.75t + t2 = 3.5 The t term is 3.75t. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75t + 3.515625 + t2 = 3.5 + 3.515625 Reorder the terms: 3.515625 + 3.75t + t2 = 3.5 + 3.515625 Combine like terms: 3.5 + 3.515625 = 7.015625 3.515625 + 3.75t + t2 = 7.015625 Factor a perfect square on the left side: (t + 1.875)(t + 1.875) = 7.015625 Calculate the square root of the right side: 2.648702513 Break this problem into two subproblems by setting (t + 1.875) equal to 2.648702513 and -2.648702513.Subproblem 1
t + 1.875 = 2.648702513 Simplifying t + 1.875 = 2.648702513 Reorder the terms: 1.875 + t = 2.648702513 Solving 1.875 + t = 2.648702513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = 2.648702513 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = 2.648702513 + -1.875 t = 2.648702513 + -1.875 Combine like terms: 2.648702513 + -1.875 = 0.773702513 t = 0.773702513 Simplifying t = 0.773702513Subproblem 2
t + 1.875 = -2.648702513 Simplifying t + 1.875 = -2.648702513 Reorder the terms: 1.875 + t = -2.648702513 Solving 1.875 + t = -2.648702513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = -2.648702513 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = -2.648702513 + -1.875 t = -2.648702513 + -1.875 Combine like terms: -2.648702513 + -1.875 = -4.523702513 t = -4.523702513 Simplifying t = -4.523702513Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.773702513, -4.523702513}
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