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Simplifying 0 = -5t2 + 30t + 12 Reorder the terms: 0 = 12 + 30t + -5t2 Solving 0 = 12 + 30t + -5t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -30t + 5t2 = 12 + 30t + -5t2 + -12 + -30t + 5t2 Reorder the terms: -12 + -30t + 5t2 = 12 + -12 + 30t + -30t + -5t2 + 5t2 Combine like terms: 12 + -12 = 0 -12 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2 -12 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2 Combine like terms: 30t + -30t = 0 -12 + -30t + 5t2 = 0 + -5t2 + 5t2 -12 + -30t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -12 + -30t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -6t + t2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -6t + 2.4 + t2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -6t + t2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -6t + t2 = 0 + 2.4 -6t + t2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -6t + t2 = 2.4 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 2.4 + 9 Reorder the terms: 9 + -6t + t2 = 2.4 + 9 Combine like terms: 2.4 + 9 = 11.4 9 + -6t + t2 = 11.4 Factor a perfect square on the left side: (t + -3)(t + -3) = 11.4 Calculate the square root of the right side: 3.376388603 Break this problem into two subproblems by setting (t + -3) equal to 3.376388603 and -3.376388603.Subproblem 1
t + -3 = 3.376388603 Simplifying t + -3 = 3.376388603 Reorder the terms: -3 + t = 3.376388603 Solving -3 + t = 3.376388603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.376388603 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.376388603 + 3 t = 3.376388603 + 3 Combine like terms: 3.376388603 + 3 = 6.376388603 t = 6.376388603 Simplifying t = 6.376388603Subproblem 2
t + -3 = -3.376388603 Simplifying t + -3 = -3.376388603 Reorder the terms: -3 + t = -3.376388603 Solving -3 + t = -3.376388603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.376388603 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.376388603 + 3 t = -3.376388603 + 3 Combine like terms: -3.376388603 + 3 = -0.376388603 t = -0.376388603 Simplifying t = -0.376388603Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.376388603, -0.376388603}
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