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Simplifying 435.75 = t2 + 70t Reorder the terms: 435.75 = 70t + t2 Solving 435.75 = 70t + t2 Solving for variable 't'. Reorder the terms: 435.75 + -70t + -1t2 = 70t + -70t + t2 + -1t2 Combine like terms: 70t + -70t = 0 435.75 + -70t + -1t2 = 0 + t2 + -1t2 435.75 + -70t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 435.75 + -70t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -435.75 + 70t + t2 = 0 Move the constant term to the right: Add '435.75' to each side of the equation. -435.75 + 70t + 435.75 + t2 = 0 + 435.75 Reorder the terms: -435.75 + 435.75 + 70t + t2 = 0 + 435.75 Combine like terms: -435.75 + 435.75 = 0.00 0.00 + 70t + t2 = 0 + 435.75 70t + t2 = 0 + 435.75 Combine like terms: 0 + 435.75 = 435.75 70t + t2 = 435.75 The t term is 70t. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70t + 1225 + t2 = 435.75 + 1225 Reorder the terms: 1225 + 70t + t2 = 435.75 + 1225 Combine like terms: 435.75 + 1225 = 1660.75 1225 + 70t + t2 = 1660.75 Factor a perfect square on the left side: (t + 35)(t + 35) = 1660.75 Calculate the square root of the right side: 40.752300549 Break this problem into two subproblems by setting (t + 35) equal to 40.752300549 and -40.752300549.Subproblem 1
t + 35 = 40.752300549 Simplifying t + 35 = 40.752300549 Reorder the terms: 35 + t = 40.752300549 Solving 35 + t = 40.752300549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + t = 40.752300549 + -35 Combine like terms: 35 + -35 = 0 0 + t = 40.752300549 + -35 t = 40.752300549 + -35 Combine like terms: 40.752300549 + -35 = 5.752300549 t = 5.752300549 Simplifying t = 5.752300549Subproblem 2
t + 35 = -40.752300549 Simplifying t + 35 = -40.752300549 Reorder the terms: 35 + t = -40.752300549 Solving 35 + t = -40.752300549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + t = -40.752300549 + -35 Combine like terms: 35 + -35 = 0 0 + t = -40.752300549 + -35 t = -40.752300549 + -35 Combine like terms: -40.752300549 + -35 = -75.752300549 t = -75.752300549 Simplifying t = -75.752300549Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.752300549, -75.752300549}
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