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Simplifying 123 + -11t + -16t2 = 0 Solving 123 + -11t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -7.6875 + 0.6875t + t2 = 0 Move the constant term to the right: Add '7.6875' to each side of the equation. -7.6875 + 0.6875t + 7.6875 + t2 = 0 + 7.6875 Reorder the terms: -7.6875 + 7.6875 + 0.6875t + t2 = 0 + 7.6875 Combine like terms: -7.6875 + 7.6875 = 0.0000 0.0000 + 0.6875t + t2 = 0 + 7.6875 0.6875t + t2 = 0 + 7.6875 Combine like terms: 0 + 7.6875 = 7.6875 0.6875t + t2 = 7.6875 The t term is 0.6875t. Take half its coefficient (0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. 0.6875t + 0.1181640625 + t2 = 7.6875 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875t + t2 = 7.6875 + 0.1181640625 Combine like terms: 7.6875 + 0.1181640625 = 7.8056640625 0.1181640625 + 0.6875t + t2 = 7.8056640625 Factor a perfect square on the left side: (t + 0.34375)(t + 0.34375) = 7.8056640625 Calculate the square root of the right side: 2.793861855 Break this problem into two subproblems by setting (t + 0.34375) equal to 2.793861855 and -2.793861855.Subproblem 1
t + 0.34375 = 2.793861855 Simplifying t + 0.34375 = 2.793861855 Reorder the terms: 0.34375 + t = 2.793861855 Solving 0.34375 + t = 2.793861855 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + t = 2.793861855 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = 2.793861855 + -0.34375 t = 2.793861855 + -0.34375 Combine like terms: 2.793861855 + -0.34375 = 2.450111855 t = 2.450111855 Simplifying t = 2.450111855Subproblem 2
t + 0.34375 = -2.793861855 Simplifying t + 0.34375 = -2.793861855 Reorder the terms: 0.34375 + t = -2.793861855 Solving 0.34375 + t = -2.793861855 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + t = -2.793861855 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = -2.793861855 + -0.34375 t = -2.793861855 + -0.34375 Combine like terms: -2.793861855 + -0.34375 = -3.137611855 t = -3.137611855 Simplifying t = -3.137611855Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.450111855, -3.137611855}
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