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Simplifying -5t2 + 12t + 14 = 0 Reorder the terms: 14 + 12t + -5t2 = 0 Solving 14 + 12t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.8 + -2.4t + t2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -2.4t + 2.8 + t2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -2.4t + t2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -2.4t + t2 = 0 + 2.8 -2.4t + t2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -2.4t + t2 = 2.8 The t term is -2.4t. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4t + 1.44 + t2 = 2.8 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = 2.8 + 1.44 Combine like terms: 2.8 + 1.44 = 4.24 1.44 + -2.4t + t2 = 4.24 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (t + -1.2) equal to 2.059126028 and -2.059126028.Subproblem 1
t + -1.2 = 2.059126028 Simplifying t + -1.2 = 2.059126028 Reorder the terms: -1.2 + t = 2.059126028 Solving -1.2 + t = 2.059126028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = 2.059126028 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 2.059126028 + 1.2 t = 2.059126028 + 1.2 Combine like terms: 2.059126028 + 1.2 = 3.259126028 t = 3.259126028 Simplifying t = 3.259126028Subproblem 2
t + -1.2 = -2.059126028 Simplifying t + -1.2 = -2.059126028 Reorder the terms: -1.2 + t = -2.059126028 Solving -1.2 + t = -2.059126028 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = -2.059126028 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -2.059126028 + 1.2 t = -2.059126028 + 1.2 Combine like terms: -2.059126028 + 1.2 = -0.859126028 t = -0.859126028 Simplifying t = -0.859126028Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.259126028, -0.859126028}
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