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Simplifying 15t2 + -2t + -12 = 0 Reorder the terms: -12 + -2t + 15t2 = 0 Solving -12 + -2t + 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'. -0.8 + -0.1333333333t + t2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.1333333333t + 0.8 + t2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.1333333333t + t2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.1333333333t + t2 = 0 + 0.8 -0.1333333333t + t2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.1333333333t + t2 = 0.8 The t term is -0.1333333333t. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333t + 0.004444444442 + t2 = 0.8 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333t + t2 = 0.8 + 0.004444444442 Combine like terms: 0.8 + 0.004444444442 = 0.804444444442 0.004444444442 + -0.1333333333t + t2 = 0.804444444442 Factor a perfect square on the left side: (t + -0.06666666665)(t + -0.06666666665) = 0.804444444442 Calculate the square root of the right side: 0.89690827 Break this problem into two subproblems by setting (t + -0.06666666665) equal to 0.89690827 and -0.89690827.Subproblem 1
t + -0.06666666665 = 0.89690827 Simplifying t + -0.06666666665 = 0.89690827 Reorder the terms: -0.06666666665 + t = 0.89690827 Solving -0.06666666665 + t = 0.89690827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + t = 0.89690827 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + t = 0.89690827 + 0.06666666665 t = 0.89690827 + 0.06666666665 Combine like terms: 0.89690827 + 0.06666666665 = 0.96357493665 t = 0.96357493665 Simplifying t = 0.96357493665Subproblem 2
t + -0.06666666665 = -0.89690827 Simplifying t + -0.06666666665 = -0.89690827 Reorder the terms: -0.06666666665 + t = -0.89690827 Solving -0.06666666665 + t = -0.89690827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + t = -0.89690827 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + t = -0.89690827 + 0.06666666665 t = -0.89690827 + 0.06666666665 Combine like terms: -0.89690827 + 0.06666666665 = -0.83024160335 t = -0.83024160335 Simplifying t = -0.83024160335Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.96357493665, -0.83024160335}
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