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Simplifying 5t + -0.2t2 = 30 Solving 5t + -0.2t2 = 30 Solving for variable 't'. Reorder the terms: -30 + 5t + -0.2t2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 5t + -0.2t2 = 0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 150 + -25t + t2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -25t + -150 + t2 = 0 + -150 Reorder the terms: 150 + -150 + -25t + t2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -25t + t2 = 0 + -150 -25t + t2 = 0 + -150 Combine like terms: 0 + -150 = -150 -25t + t2 = -150 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = -150 + 156.25 Reorder the terms: 156.25 + -25t + t2 = -150 + 156.25 Combine like terms: -150 + 156.25 = 6.25 156.25 + -25t + t2 = 6.25 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (t + -12.5) equal to 2.5 and -2.5.Subproblem 1
t + -12.5 = 2.5 Simplifying t + -12.5 = 2.5 Reorder the terms: -12.5 + t = 2.5 Solving -12.5 + t = 2.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 2.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 2.5 + 12.5 t = 2.5 + 12.5 Combine like terms: 2.5 + 12.5 = 15 t = 15 Simplifying t = 15Subproblem 2
t + -12.5 = -2.5 Simplifying t + -12.5 = -2.5 Reorder the terms: -12.5 + t = -2.5 Solving -12.5 + t = -2.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -2.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -2.5 + 12.5 t = -2.5 + 12.5 Combine like terms: -2.5 + 12.5 = 10 t = 10 Simplifying t = 10Solution
The solution to the problem is based on the solutions from the subproblems. t = {15, 10}
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