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Simplifying 5t2 + -80t + -8 = 0 Reorder the terms: -8 + -80t + 5t2 = 0 Solving -8 + -80t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -16t + t2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -16t + 1.6 + t2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -16t + t2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -16t + t2 = 0 + 1.6 -16t + t2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -16t + t2 = 1.6 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = 1.6 + 64 Reorder the terms: 64 + -16t + t2 = 1.6 + 64 Combine like terms: 1.6 + 64 = 65.6 64 + -16t + t2 = 65.6 Factor a perfect square on the left side: (t + -8)(t + -8) = 65.6 Calculate the square root of the right side: 8.099382693 Break this problem into two subproblems by setting (t + -8) equal to 8.099382693 and -8.099382693.Subproblem 1
t + -8 = 8.099382693 Simplifying t + -8 = 8.099382693 Reorder the terms: -8 + t = 8.099382693 Solving -8 + t = 8.099382693 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 8.099382693 + 8 Combine like terms: -8 + 8 = 0 0 + t = 8.099382693 + 8 t = 8.099382693 + 8 Combine like terms: 8.099382693 + 8 = 16.099382693 t = 16.099382693 Simplifying t = 16.099382693Subproblem 2
t + -8 = -8.099382693 Simplifying t + -8 = -8.099382693 Reorder the terms: -8 + t = -8.099382693 Solving -8 + t = -8.099382693 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -8.099382693 + 8 Combine like terms: -8 + 8 = 0 0 + t = -8.099382693 + 8 t = -8.099382693 + 8 Combine like terms: -8.099382693 + 8 = -0.099382693 t = -0.099382693 Simplifying t = -0.099382693Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.099382693, -0.099382693}
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