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Simplifying 0.2t2 + -3t + -8.75 = 0 Reorder the terms: -8.75 + -3t + 0.2t2 = 0 Solving -8.75 + -3t + 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'. -43.75 + -15t + t2 = 0 Move the constant term to the right: Add '43.75' to each side of the equation. -43.75 + -15t + 43.75 + t2 = 0 + 43.75 Reorder the terms: -43.75 + 43.75 + -15t + t2 = 0 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + -15t + t2 = 0 + 43.75 -15t + t2 = 0 + 43.75 Combine like terms: 0 + 43.75 = 43.75 -15t + t2 = 43.75 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = 43.75 + 56.25 Reorder the terms: 56.25 + -15t + t2 = 43.75 + 56.25 Combine like terms: 43.75 + 56.25 = 100 56.25 + -15t + t2 = 100 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (t + -7.5) equal to 10 and -10.Subproblem 1
t + -7.5 = 10 Simplifying t + -7.5 = 10 Reorder the terms: -7.5 + t = 10 Solving -7.5 + t = 10 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 10 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 10 + 7.5 t = 10 + 7.5 Combine like terms: 10 + 7.5 = 17.5 t = 17.5 Simplifying t = 17.5Subproblem 2
t + -7.5 = -10 Simplifying t + -7.5 = -10 Reorder the terms: -7.5 + t = -10 Solving -7.5 + t = -10 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -10 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -10 + 7.5 t = -10 + 7.5 Combine like terms: -10 + 7.5 = -2.5 t = -2.5 Simplifying t = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.5, -2.5}
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