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Simplifying 8t2 + 19t = 6 Reorder the terms: 19t + 8t2 = 6 Solving 19t + 8t2 = 6 Solving for variable 't'. Reorder the terms: -6 + 19t + 8t2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 19t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + 2.375t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 2.375t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 2.375t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 2.375t + t2 = 0 + 0.75 2.375t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 2.375t + t2 = 0.75 The t term is 2.375t. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375t + 1.41015625 + t2 = 0.75 + 1.41015625 Reorder the terms: 1.41015625 + 2.375t + t2 = 0.75 + 1.41015625 Combine like terms: 0.75 + 1.41015625 = 2.16015625 1.41015625 + 2.375t + t2 = 2.16015625 Factor a perfect square on the left side: (t + 1.1875)(t + 1.1875) = 2.16015625 Calculate the square root of the right side: 1.469747002 Break this problem into two subproblems by setting (t + 1.1875) equal to 1.469747002 and -1.469747002.Subproblem 1
t + 1.1875 = 1.469747002 Simplifying t + 1.1875 = 1.469747002 Reorder the terms: 1.1875 + t = 1.469747002 Solving 1.1875 + t = 1.469747002 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = 1.469747002 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = 1.469747002 + -1.1875 t = 1.469747002 + -1.1875 Combine like terms: 1.469747002 + -1.1875 = 0.282247002 t = 0.282247002 Simplifying t = 0.282247002Subproblem 2
t + 1.1875 = -1.469747002 Simplifying t + 1.1875 = -1.469747002 Reorder the terms: 1.1875 + t = -1.469747002 Solving 1.1875 + t = -1.469747002 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + t = -1.469747002 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + t = -1.469747002 + -1.1875 t = -1.469747002 + -1.1875 Combine like terms: -1.469747002 + -1.1875 = -2.657247002 t = -2.657247002 Simplifying t = -2.657247002Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.282247002, -2.657247002}
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