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Simplifying 12t2 + -37t + 10 = 0 Reorder the terms: 10 + -37t + 12t2 = 0 Solving 10 + -37t + 12t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.8333333333 + -3.083333333t + t2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -3.083333333t + -0.8333333333 + t2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -3.083333333t + t2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -3.083333333t + t2 = 0 + -0.8333333333 -3.083333333t + t2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -3.083333333t + t2 = -0.8333333333 The t term is -3.083333333t. Take half its coefficient (-1.541666667). Square it (2.376736112) and add it to both sides. Add '2.376736112' to each side of the equation. -3.083333333t + 2.376736112 + t2 = -0.8333333333 + 2.376736112 Reorder the terms: 2.376736112 + -3.083333333t + t2 = -0.8333333333 + 2.376736112 Combine like terms: -0.8333333333 + 2.376736112 = 1.5434027787 2.376736112 + -3.083333333t + t2 = 1.5434027787 Factor a perfect square on the left side: (t + -1.541666667)(t + -1.541666667) = 1.5434027787 Calculate the square root of the right side: 1.242337627 Break this problem into two subproblems by setting (t + -1.541666667) equal to 1.242337627 and -1.242337627.Subproblem 1
t + -1.541666667 = 1.242337627 Simplifying t + -1.541666667 = 1.242337627 Reorder the terms: -1.541666667 + t = 1.242337627 Solving -1.541666667 + t = 1.242337627 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.541666667' to each side of the equation. -1.541666667 + 1.541666667 + t = 1.242337627 + 1.541666667 Combine like terms: -1.541666667 + 1.541666667 = 0.000000000 0.000000000 + t = 1.242337627 + 1.541666667 t = 1.242337627 + 1.541666667 Combine like terms: 1.242337627 + 1.541666667 = 2.784004294 t = 2.784004294 Simplifying t = 2.784004294Subproblem 2
t + -1.541666667 = -1.242337627 Simplifying t + -1.541666667 = -1.242337627 Reorder the terms: -1.541666667 + t = -1.242337627 Solving -1.541666667 + t = -1.242337627 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.541666667' to each side of the equation. -1.541666667 + 1.541666667 + t = -1.242337627 + 1.541666667 Combine like terms: -1.541666667 + 1.541666667 = 0.000000000 0.000000000 + t = -1.242337627 + 1.541666667 t = -1.242337627 + 1.541666667 Combine like terms: -1.242337627 + 1.541666667 = 0.29932904 t = 0.29932904 Simplifying t = 0.29932904Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.784004294, 0.29932904}
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