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Simplifying -0.2t2 + 4t + -7.2 = 0 Reorder the terms: -7.2 + 4t + -0.2t2 = 0 Solving -7.2 + 4t + -0.2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 36 + -20t + t2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -20t + -36 + t2 = 0 + -36 Reorder the terms: 36 + -36 + -20t + t2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -20t + t2 = 0 + -36 -20t + t2 = 0 + -36 Combine like terms: 0 + -36 = -36 -20t + t2 = -36 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = -36 + 100 Reorder the terms: 100 + -20t + t2 = -36 + 100 Combine like terms: -36 + 100 = 64 100 + -20t + t2 = 64 Factor a perfect square on the left side: (t + -10)(t + -10) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (t + -10) equal to 8 and -8.Subproblem 1
t + -10 = 8 Simplifying t + -10 = 8 Reorder the terms: -10 + t = 8 Solving -10 + t = 8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 8 + 10 Combine like terms: -10 + 10 = 0 0 + t = 8 + 10 t = 8 + 10 Combine like terms: 8 + 10 = 18 t = 18 Simplifying t = 18Subproblem 2
t + -10 = -8 Simplifying t + -10 = -8 Reorder the terms: -10 + t = -8 Solving -10 + t = -8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -8 + 10 Combine like terms: -10 + 10 = 0 0 + t = -8 + 10 t = -8 + 10 Combine like terms: -8 + 10 = 2 t = 2 Simplifying t = 2Solution
The solution to the problem is based on the solutions from the subproblems. t = {18, 2}
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