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Simplifying -4.67(t2) + 1.72t + 50 = 0 Reorder the terms: 50 + 1.72t + -4.67t2 = 0 Solving 50 + 1.72t + -4.67t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.67 the coefficient of the squared term: Divide each side by '-4.67'. -10.70663812 + -0.3683083512t + t2 = 0 Move the constant term to the right: Add '10.70663812' to each side of the equation. -10.70663812 + -0.3683083512t + 10.70663812 + t2 = 0 + 10.70663812 Reorder the terms: -10.70663812 + 10.70663812 + -0.3683083512t + t2 = 0 + 10.70663812 Combine like terms: -10.70663812 + 10.70663812 = 0.00000000 0.00000000 + -0.3683083512t + t2 = 0 + 10.70663812 -0.3683083512t + t2 = 0 + 10.70663812 Combine like terms: 0 + 10.70663812 = 10.70663812 -0.3683083512t + t2 = 10.70663812 The t term is -0.3683083512t. Take half its coefficient (-0.1841541756). Square it (0.03391276039) and add it to both sides. Add '0.03391276039' to each side of the equation. -0.3683083512t + 0.03391276039 + t2 = 10.70663812 + 0.03391276039 Reorder the terms: 0.03391276039 + -0.3683083512t + t2 = 10.70663812 + 0.03391276039 Combine like terms: 10.70663812 + 0.03391276039 = 10.74055088039 0.03391276039 + -0.3683083512t + t2 = 10.74055088039 Factor a perfect square on the left side: (t + -0.1841541756)(t + -0.1841541756) = 10.74055088039 Calculate the square root of the right side: 3.277277968 Break this problem into two subproblems by setting (t + -0.1841541756) equal to 3.277277968 and -3.277277968.Subproblem 1
t + -0.1841541756 = 3.277277968 Simplifying t + -0.1841541756 = 3.277277968 Reorder the terms: -0.1841541756 + t = 3.277277968 Solving -0.1841541756 + t = 3.277277968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1841541756' to each side of the equation. -0.1841541756 + 0.1841541756 + t = 3.277277968 + 0.1841541756 Combine like terms: -0.1841541756 + 0.1841541756 = 0.0000000000 0.0000000000 + t = 3.277277968 + 0.1841541756 t = 3.277277968 + 0.1841541756 Combine like terms: 3.277277968 + 0.1841541756 = 3.4614321436 t = 3.4614321436 Simplifying t = 3.4614321436Subproblem 2
t + -0.1841541756 = -3.277277968 Simplifying t + -0.1841541756 = -3.277277968 Reorder the terms: -0.1841541756 + t = -3.277277968 Solving -0.1841541756 + t = -3.277277968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1841541756' to each side of the equation. -0.1841541756 + 0.1841541756 + t = -3.277277968 + 0.1841541756 Combine like terms: -0.1841541756 + 0.1841541756 = 0.0000000000 0.0000000000 + t = -3.277277968 + 0.1841541756 t = -3.277277968 + 0.1841541756 Combine like terms: -3.277277968 + 0.1841541756 = -3.0931237924 t = -3.0931237924 Simplifying t = -3.0931237924Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.4614321436, -3.0931237924}
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