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Simplifying 30t2 + -15t + -4 = 0 Reorder the terms: -4 + -15t + 30t2 = 0 Solving -4 + -15t + 30t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.1333333333 + -0.5t + t2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + -0.5t + 0.1333333333 + t2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + -0.5t + t2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + -0.5t + t2 = 0 + 0.1333333333 -0.5t + t2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 -0.5t + t2 = 0.1333333333 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 0.1333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 0.1333333333 + 0.0625 Combine like terms: 0.1333333333 + 0.0625 = 0.1958333333 0.0625 + -0.5t + t2 = 0.1958333333 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 0.1958333333 Calculate the square root of the right side: 0.442530602 Break this problem into two subproblems by setting (t + -0.25) equal to 0.442530602 and -0.442530602.Subproblem 1
t + -0.25 = 0.442530602 Simplifying t + -0.25 = 0.442530602 Reorder the terms: -0.25 + t = 0.442530602 Solving -0.25 + t = 0.442530602 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 0.442530602 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 0.442530602 + 0.25 t = 0.442530602 + 0.25 Combine like terms: 0.442530602 + 0.25 = 0.692530602 t = 0.692530602 Simplifying t = 0.692530602Subproblem 2
t + -0.25 = -0.442530602 Simplifying t + -0.25 = -0.442530602 Reorder the terms: -0.25 + t = -0.442530602 Solving -0.25 + t = -0.442530602 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -0.442530602 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -0.442530602 + 0.25 t = -0.442530602 + 0.25 Combine like terms: -0.442530602 + 0.25 = -0.192530602 t = -0.192530602 Simplifying t = -0.192530602Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.692530602, -0.192530602}
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