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Simplifying 8t2 + -48t + -95 = 0 Reorder the terms: -95 + -48t + 8t2 = 0 Solving -95 + -48t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.875 + -6t + t2 = 0 Move the constant term to the right: Add '11.875' to each side of the equation. -11.875 + -6t + 11.875 + t2 = 0 + 11.875 Reorder the terms: -11.875 + 11.875 + -6t + t2 = 0 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + -6t + t2 = 0 + 11.875 -6t + t2 = 0 + 11.875 Combine like terms: 0 + 11.875 = 11.875 -6t + t2 = 11.875 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 11.875 + 9 Reorder the terms: 9 + -6t + t2 = 11.875 + 9 Combine like terms: 11.875 + 9 = 20.875 9 + -6t + t2 = 20.875 Factor a perfect square on the left side: (t + -3)(t + -3) = 20.875 Calculate the square root of the right side: 4.568916721 Break this problem into two subproblems by setting (t + -3) equal to 4.568916721 and -4.568916721.Subproblem 1
t + -3 = 4.568916721 Simplifying t + -3 = 4.568916721 Reorder the terms: -3 + t = 4.568916721 Solving -3 + t = 4.568916721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 4.568916721 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.568916721 + 3 t = 4.568916721 + 3 Combine like terms: 4.568916721 + 3 = 7.568916721 t = 7.568916721 Simplifying t = 7.568916721Subproblem 2
t + -3 = -4.568916721 Simplifying t + -3 = -4.568916721 Reorder the terms: -3 + t = -4.568916721 Solving -3 + t = -4.568916721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -4.568916721 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.568916721 + 3 t = -4.568916721 + 3 Combine like terms: -4.568916721 + 3 = -1.568916721 t = -1.568916721 Simplifying t = -1.568916721Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.568916721, -1.568916721}
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