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Simplifying 15t2 + 9t + -2 = 0 Reorder the terms: -2 + 9t + 15t2 = 0 Solving -2 + 9t + 15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.1333333333 + 0.6t + t2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + 0.6t + 0.1333333333 + t2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + 0.6t + t2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + 0.6t + t2 = 0 + 0.1333333333 0.6t + t2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 0.6t + t2 = 0.1333333333 The t term is 0.6t. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6t + 0.09 + t2 = 0.1333333333 + 0.09 Reorder the terms: 0.09 + 0.6t + t2 = 0.1333333333 + 0.09 Combine like terms: 0.1333333333 + 0.09 = 0.2233333333 0.09 + 0.6t + t2 = 0.2233333333 Factor a perfect square on the left side: (t + 0.3)(t + 0.3) = 0.2233333333 Calculate the square root of the right side: 0.472581563 Break this problem into two subproblems by setting (t + 0.3) equal to 0.472581563 and -0.472581563.Subproblem 1
t + 0.3 = 0.472581563 Simplifying t + 0.3 = 0.472581563 Reorder the terms: 0.3 + t = 0.472581563 Solving 0.3 + t = 0.472581563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + t = 0.472581563 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + t = 0.472581563 + -0.3 t = 0.472581563 + -0.3 Combine like terms: 0.472581563 + -0.3 = 0.172581563 t = 0.172581563 Simplifying t = 0.172581563Subproblem 2
t + 0.3 = -0.472581563 Simplifying t + 0.3 = -0.472581563 Reorder the terms: 0.3 + t = -0.472581563 Solving 0.3 + t = -0.472581563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + t = -0.472581563 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + t = -0.472581563 + -0.3 t = -0.472581563 + -0.3 Combine like terms: -0.472581563 + -0.3 = -0.772581563 t = -0.772581563 Simplifying t = -0.772581563Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.172581563, -0.772581563}
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