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Simplifying 35t + -5t2 = 12 Solving 35t + -5t2 = 12 Solving for variable 't'. Reorder the terms: -12 + 35t + -5t2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 35t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.4 + -7t + t2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -7t + -2.4 + t2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -7t + t2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -7t + t2 = 0 + -2.4 -7t + t2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -7t + t2 = -2.4 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -2.4 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -2.4 + 12.25 Combine like terms: -2.4 + 12.25 = 9.85 12.25 + -7t + t2 = 9.85 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 9.85 Calculate the square root of the right side: 3.138470965 Break this problem into two subproblems by setting (t + -3.5) equal to 3.138470965 and -3.138470965.Subproblem 1
t + -3.5 = 3.138470965 Simplifying t + -3.5 = 3.138470965 Reorder the terms: -3.5 + t = 3.138470965 Solving -3.5 + t = 3.138470965 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.138470965 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.138470965 + 3.5 t = 3.138470965 + 3.5 Combine like terms: 3.138470965 + 3.5 = 6.638470965 t = 6.638470965 Simplifying t = 6.638470965Subproblem 2
t + -3.5 = -3.138470965 Simplifying t + -3.5 = -3.138470965 Reorder the terms: -3.5 + t = -3.138470965 Solving -3.5 + t = -3.138470965 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.138470965 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.138470965 + 3.5 t = -3.138470965 + 3.5 Combine like terms: -3.138470965 + 3.5 = 0.361529035 t = 0.361529035 Simplifying t = 0.361529035Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.638470965, 0.361529035}
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