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Simplifying 0 = t2 + -6t + -0.4375 Reorder the terms: 0 = -0.4375 + -6t + t2 Solving 0 = -0.4375 + -6t + t2 Solving for variable 't'. Combine like terms: 0 + 0.4375 = 0.4375 0.4375 + 6t + -1t2 = -0.4375 + -6t + t2 + 0.4375 + 6t + -1t2 Reorder the terms: 0.4375 + 6t + -1t2 = -0.4375 + 0.4375 + -6t + 6t + t2 + -1t2 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.4375 + 6t + -1t2 = 0.0000 + -6t + 6t + t2 + -1t2 0.4375 + 6t + -1t2 = -6t + 6t + t2 + -1t2 Combine like terms: -6t + 6t = 0 0.4375 + 6t + -1t2 = 0 + t2 + -1t2 0.4375 + 6t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 0.4375 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.4375 + -6t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -6t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -6t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -6t + t2 = 0 + 0.4375 -6t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -6t + t2 = 0.4375 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 = 0.4375 + 9 Reorder the terms: 9 + -6t + t2 = 0.4375 + 9 Combine like terms: 0.4375 + 9 = 9.4375 9 + -6t + t2 = 9.4375 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.4375 Calculate the square root of the right side: 3.072051432 Break this problem into two subproblems by setting (t + -3) equal to 3.072051432 and -3.072051432.Subproblem 1
t + -3 = 3.072051432 Simplifying t + -3 = 3.072051432 Reorder the terms: -3 + t = 3.072051432 Solving -3 + t = 3.072051432 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 = 3.072051432 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.072051432 + 3 t = 3.072051432 + 3 Combine like terms: 3.072051432 + 3 = 6.072051432 t = 6.072051432 Simplifying t = 6.072051432Subproblem 2
t + -3 = -3.072051432 Simplifying t + -3 = -3.072051432 Reorder the terms: -3 + t = -3.072051432 Solving -3 + t = -3.072051432 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 = -3.072051432 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.072051432 + 3 t = -3.072051432 + 3 Combine like terms: -3.072051432 + 3 = -0.072051432 t = -0.072051432 Simplifying t = -0.072051432Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.072051432, -0.072051432}
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