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Simplifying 0 = 16t2 + 95t + 6 Reorder the terms: 0 = 6 + 95t + 16t2 Solving 0 = 6 + 95t + 16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -95t + -16t2 = 6 + 95t + 16t2 + -6 + -95t + -16t2 Reorder the terms: -6 + -95t + -16t2 = 6 + -6 + 95t + -95t + 16t2 + -16t2 Combine like terms: 6 + -6 = 0 -6 + -95t + -16t2 = 0 + 95t + -95t + 16t2 + -16t2 -6 + -95t + -16t2 = 95t + -95t + 16t2 + -16t2 Combine like terms: 95t + -95t = 0 -6 + -95t + -16t2 = 0 + 16t2 + -16t2 -6 + -95t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -6 + -95t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 95t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 95t + 16t2)' equal to zero and attempt to solve: Simplifying 6 + 95t + 16t2 = 0 Solving 6 + 95t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.375 + 5.9375t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 5.9375t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 5.9375t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 5.9375t + t2 = 0 + -0.375 5.9375t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 5.9375t + t2 = -0.375 The t term is 5.9375t. Take half its coefficient (2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. 5.9375t + 8.813476563 + t2 = -0.375 + 8.813476563 Reorder the terms: 8.813476563 + 5.9375t + t2 = -0.375 + 8.813476563 Combine like terms: -0.375 + 8.813476563 = 8.438476563 8.813476563 + 5.9375t + t2 = 8.438476563 Factor a perfect square on the left side: (t + 2.96875)(t + 2.96875) = 8.438476563 Calculate the square root of the right side: 2.904905603 Break this problem into two subproblems by setting (t + 2.96875) equal to 2.904905603 and -2.904905603.Subproblem 1
t + 2.96875 = 2.904905603 Simplifying t + 2.96875 = 2.904905603 Reorder the terms: 2.96875 + t = 2.904905603 Solving 2.96875 + t = 2.904905603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.96875' to each side of the equation. 2.96875 + -2.96875 + t = 2.904905603 + -2.96875 Combine like terms: 2.96875 + -2.96875 = 0.00000 0.00000 + t = 2.904905603 + -2.96875 t = 2.904905603 + -2.96875 Combine like terms: 2.904905603 + -2.96875 = -0.063844397 t = -0.063844397 Simplifying t = -0.063844397Subproblem 2
t + 2.96875 = -2.904905603 Simplifying t + 2.96875 = -2.904905603 Reorder the terms: 2.96875 + t = -2.904905603 Solving 2.96875 + t = -2.904905603 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.96875' to each side of the equation. 2.96875 + -2.96875 + t = -2.904905603 + -2.96875 Combine like terms: 2.96875 + -2.96875 = 0.00000 0.00000 + t = -2.904905603 + -2.96875 t = -2.904905603 + -2.96875 Combine like terms: -2.904905603 + -2.96875 = -5.873655603 t = -5.873655603 Simplifying t = -5.873655603Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.063844397, -5.873655603}Solution
t = {-0.063844397, -5.873655603}
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