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Simplifying 10 = 110 + -6t + -16t2 Solving 10 = 110 + -6t + -16t2 Solving for variable 't'. Combine like terms: 10 + -110 = -100 -100 + 6t + 16t2 = 110 + -6t + -16t2 + -110 + 6t + 16t2 Reorder the terms: -100 + 6t + 16t2 = 110 + -110 + -6t + 6t + -16t2 + 16t2 Combine like terms: 110 + -110 = 0 -100 + 6t + 16t2 = 0 + -6t + 6t + -16t2 + 16t2 -100 + 6t + 16t2 = -6t + 6t + -16t2 + 16t2 Combine like terms: -6t + 6t = 0 -100 + 6t + 16t2 = 0 + -16t2 + 16t2 -100 + 6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + 6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 3t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 3t + 8t2)' equal to zero and attempt to solve: Simplifying -50 + 3t + 8t2 = 0 Solving -50 + 3t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.25 + 0.375t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.375t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.375t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.375t + t2 = 0 + 6.25 0.375t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.375t + t2 = 6.25 The t term is 0.375t. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375t + 0.03515625 + t2 = 6.25 + 0.03515625 Reorder the terms: 0.03515625 + 0.375t + t2 = 6.25 + 0.03515625 Combine like terms: 6.25 + 0.03515625 = 6.28515625 0.03515625 + 0.375t + t2 = 6.28515625 Factor a perfect square on the left side: (t + 0.1875)(t + 0.1875) = 6.28515625 Calculate the square root of the right side: 2.50702139 Break this problem into two subproblems by setting (t + 0.1875) equal to 2.50702139 and -2.50702139.Subproblem 1
t + 0.1875 = 2.50702139 Simplifying t + 0.1875 = 2.50702139 Reorder the terms: 0.1875 + t = 2.50702139 Solving 0.1875 + t = 2.50702139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + t = 2.50702139 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + t = 2.50702139 + -0.1875 t = 2.50702139 + -0.1875 Combine like terms: 2.50702139 + -0.1875 = 2.31952139 t = 2.31952139 Simplifying t = 2.31952139Subproblem 2
t + 0.1875 = -2.50702139 Simplifying t + 0.1875 = -2.50702139 Reorder the terms: 0.1875 + t = -2.50702139 Solving 0.1875 + t = -2.50702139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + t = -2.50702139 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + t = -2.50702139 + -0.1875 t = -2.50702139 + -0.1875 Combine like terms: -2.50702139 + -0.1875 = -2.69452139 t = -2.69452139 Simplifying t = -2.69452139Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.31952139, -2.69452139}Solution
t = {2.31952139, -2.69452139}
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