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Simplifying 8t2 + -10t + 1 = 0 Reorder the terms: 1 + -10t + 8t2 = 0 Solving 1 + -10t + 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'. 0.125 + -1.25t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1.25t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1.25t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1.25t + t2 = 0 + -0.125 -1.25t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1.25t + t2 = -0.125 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = -0.125 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = -0.125 + 0.390625 Combine like terms: -0.125 + 0.390625 = 0.265625 0.390625 + -1.25t + t2 = 0.265625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (t + -0.625) equal to 0.515388203 and -0.515388203.Subproblem 1
t + -0.625 = 0.515388203 Simplifying t + -0.625 = 0.515388203 Reorder the terms: -0.625 + t = 0.515388203 Solving -0.625 + t = 0.515388203 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 0.515388203 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 0.515388203 + 0.625 t = 0.515388203 + 0.625 Combine like terms: 0.515388203 + 0.625 = 1.140388203 t = 1.140388203 Simplifying t = 1.140388203Subproblem 2
t + -0.625 = -0.515388203 Simplifying t + -0.625 = -0.515388203 Reorder the terms: -0.625 + t = -0.515388203 Solving -0.625 + t = -0.515388203 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -0.515388203 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -0.515388203 + 0.625 t = -0.515388203 + 0.625 Combine like terms: -0.515388203 + 0.625 = 0.109611797 t = 0.109611797 Simplifying t = 0.109611797Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.140388203, 0.109611797}
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