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Simplifying 240 = 390 + -5t2 + 2t Reorder the terms: 240 = 390 + 2t + -5t2 Solving 240 = 390 + 2t + -5t2 Solving for variable 't'. Combine like terms: 240 + -390 = -150 -150 + -2t + 5t2 = 390 + 2t + -5t2 + -390 + -2t + 5t2 Reorder the terms: -150 + -2t + 5t2 = 390 + -390 + 2t + -2t + -5t2 + 5t2 Combine like terms: 390 + -390 = 0 -150 + -2t + 5t2 = 0 + 2t + -2t + -5t2 + 5t2 -150 + -2t + 5t2 = 2t + -2t + -5t2 + 5t2 Combine like terms: 2t + -2t = 0 -150 + -2t + 5t2 = 0 + -5t2 + 5t2 -150 + -2t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -150 + -2t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -30 + -0.4t + t2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -0.4t + 30 + t2 = 0 + 30 Reorder the terms: -30 + 30 + -0.4t + t2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -0.4t + t2 = 0 + 30 -0.4t + t2 = 0 + 30 Combine like terms: 0 + 30 = 30 -0.4t + t2 = 30 The t term is -0.4t. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4t + 0.04 + t2 = 30 + 0.04 Reorder the terms: 0.04 + -0.4t + t2 = 30 + 0.04 Combine like terms: 30 + 0.04 = 30.04 0.04 + -0.4t + t2 = 30.04 Factor a perfect square on the left side: (t + -0.2)(t + -0.2) = 30.04 Calculate the square root of the right side: 5.480875842 Break this problem into two subproblems by setting (t + -0.2) equal to 5.480875842 and -5.480875842.Subproblem 1
t + -0.2 = 5.480875842 Simplifying t + -0.2 = 5.480875842 Reorder the terms: -0.2 + t = 5.480875842 Solving -0.2 + t = 5.480875842 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = 5.480875842 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = 5.480875842 + 0.2 t = 5.480875842 + 0.2 Combine like terms: 5.480875842 + 0.2 = 5.680875842 t = 5.680875842 Simplifying t = 5.680875842Subproblem 2
t + -0.2 = -5.480875842 Simplifying t + -0.2 = -5.480875842 Reorder the terms: -0.2 + t = -5.480875842 Solving -0.2 + t = -5.480875842 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = -5.480875842 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = -5.480875842 + 0.2 t = -5.480875842 + 0.2 Combine like terms: -5.480875842 + 0.2 = -5.280875842 t = -5.280875842 Simplifying t = -5.280875842Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.680875842, -5.280875842}
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