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Simplifying 0 = t2 + -7.5t + -20 Reorder the terms: 0 = -20 + -7.5t + t2 Solving 0 = -20 + -7.5t + t2 Solving for variable 't'. Combine like terms: 0 + 20 = 20 20 + 7.5t + -1t2 = -20 + -7.5t + t2 + 20 + 7.5t + -1t2 Reorder the terms: 20 + 7.5t + -1t2 = -20 + 20 + -7.5t + 7.5t + t2 + -1t2 Combine like terms: -20 + 20 = 0 20 + 7.5t + -1t2 = 0 + -7.5t + 7.5t + t2 + -1t2 20 + 7.5t + -1t2 = -7.5t + 7.5t + t2 + -1t2 Combine like terms: -7.5t + 7.5t = 0.0 20 + 7.5t + -1t2 = 0.0 + t2 + -1t2 20 + 7.5t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 20 + 7.5t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -7.5t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -7.5t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -7.5t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -7.5t + t2 = 0 + 20 -7.5t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -7.5t + t2 = 20 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = 20 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = 20 + 14.0625 Combine like terms: 20 + 14.0625 = 34.0625 14.0625 + -7.5t + t2 = 34.0625 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 34.0625 Calculate the square root of the right side: 5.836308765 Break this problem into two subproblems by setting (t + -3.75) equal to 5.836308765 and -5.836308765.Subproblem 1
t + -3.75 = 5.836308765 Simplifying t + -3.75 = 5.836308765 Reorder the terms: -3.75 + t = 5.836308765 Solving -3.75 + t = 5.836308765 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 5.836308765 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 5.836308765 + 3.75 t = 5.836308765 + 3.75 Combine like terms: 5.836308765 + 3.75 = 9.586308765 t = 9.586308765 Simplifying t = 9.586308765Subproblem 2
t + -3.75 = -5.836308765 Simplifying t + -3.75 = -5.836308765 Reorder the terms: -3.75 + t = -5.836308765 Solving -3.75 + t = -5.836308765 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -5.836308765 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -5.836308765 + 3.75 t = -5.836308765 + 3.75 Combine like terms: -5.836308765 + 3.75 = -2.086308765 t = -2.086308765 Simplifying t = -2.086308765Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.586308765, -2.086308765}
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