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Simplifying 8t2 + -20t + 5 = 0 Reorder the terms: 5 + -20t + 8t2 = 0 Solving 5 + -20t + 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'. 0.625 + -2.5t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -2.5t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -2.5t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -2.5t + t2 = 0 + -0.625 -2.5t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -2.5t + t2 = -0.625 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = -0.625 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = -0.625 + 1.5625 Combine like terms: -0.625 + 1.5625 = 0.9375 1.5625 + -2.5t + t2 = 0.9375 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 0.9375 Calculate the square root of the right side: 0.968245837 Break this problem into two subproblems by setting (t + -1.25) equal to 0.968245837 and -0.968245837.Subproblem 1
t + -1.25 = 0.968245837 Simplifying t + -1.25 = 0.968245837 Reorder the terms: -1.25 + t = 0.968245837 Solving -1.25 + t = 0.968245837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 0.968245837 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 0.968245837 + 1.25 t = 0.968245837 + 1.25 Combine like terms: 0.968245837 + 1.25 = 2.218245837 t = 2.218245837 Simplifying t = 2.218245837Subproblem 2
t + -1.25 = -0.968245837 Simplifying t + -1.25 = -0.968245837 Reorder the terms: -1.25 + t = -0.968245837 Solving -1.25 + t = -0.968245837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -0.968245837 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -0.968245837 + 1.25 t = -0.968245837 + 1.25 Combine like terms: -0.968245837 + 1.25 = 0.281754163 t = 0.281754163 Simplifying t = 0.281754163Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.218245837, 0.281754163}
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