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Simplifying -4t2 + 48t + 3 = 0 Reorder the terms: 3 + 48t + -4t2 = 0 Solving 3 + 48t + -4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -12t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -12t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -12t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -12t + t2 = 0 + 0.75 -12t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -12t + t2 = 0.75 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 0.75 + 36 Reorder the terms: 36 + -12t + t2 = 0.75 + 36 Combine like terms: 0.75 + 36 = 36.75 36 + -12t + t2 = 36.75 Factor a perfect square on the left side: (t + -6)(t + -6) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (t + -6) equal to 6.062177826 and -6.062177826.Subproblem 1
t + -6 = 6.062177826 Simplifying t + -6 = 6.062177826 Reorder the terms: -6 + t = 6.062177826 Solving -6 + t = 6.062177826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 6.062177826 + 6 Combine like terms: -6 + 6 = 0 0 + t = 6.062177826 + 6 t = 6.062177826 + 6 Combine like terms: 6.062177826 + 6 = 12.062177826 t = 12.062177826 Simplifying t = 12.062177826Subproblem 2
t + -6 = -6.062177826 Simplifying t + -6 = -6.062177826 Reorder the terms: -6 + t = -6.062177826 Solving -6 + t = -6.062177826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -6.062177826 + 6 Combine like terms: -6 + 6 = 0 0 + t = -6.062177826 + 6 t = -6.062177826 + 6 Combine like terms: -6.062177826 + 6 = -0.062177826 t = -0.062177826 Simplifying t = -0.062177826Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.062177826, -0.062177826}
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