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Simplifying 2t2 + -14t + 15 = 0 Reorder the terms: 15 + -14t + 2t2 = 0 Solving 15 + -14t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -7t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -7t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -7t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -7t + t2 = 0 + -7.5 -7t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -7t + t2 = -7.5 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -7.5 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -7.5 + 12.25 Combine like terms: -7.5 + 12.25 = 4.75 12.25 + -7t + t2 = 4.75 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (t + -3.5) equal to 2.179449472 and -2.179449472.Subproblem 1
t + -3.5 = 2.179449472 Simplifying t + -3.5 = 2.179449472 Reorder the terms: -3.5 + t = 2.179449472 Solving -3.5 + t = 2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 2.179449472 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 2.179449472 + 3.5 t = 2.179449472 + 3.5 Combine like terms: 2.179449472 + 3.5 = 5.679449472 t = 5.679449472 Simplifying t = 5.679449472Subproblem 2
t + -3.5 = -2.179449472 Simplifying t + -3.5 = -2.179449472 Reorder the terms: -3.5 + t = -2.179449472 Solving -3.5 + t = -2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -2.179449472 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -2.179449472 + 3.5 t = -2.179449472 + 3.5 Combine like terms: -2.179449472 + 3.5 = 1.320550528 t = 1.320550528 Simplifying t = 1.320550528Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.679449472, 1.320550528}
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