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Simplifying 0 = -16t2 + 122t + 6 Reorder the terms: 0 = 6 + 122t + -16t2 Solving 0 = 6 + 122t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -122t + 16t2 = 6 + 122t + -16t2 + -6 + -122t + 16t2 Reorder the terms: -6 + -122t + 16t2 = 6 + -6 + 122t + -122t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -122t + 16t2 = 0 + 122t + -122t + -16t2 + 16t2 -6 + -122t + 16t2 = 122t + -122t + -16t2 + 16t2 Combine like terms: 122t + -122t = 0 -6 + -122t + 16t2 = 0 + -16t2 + 16t2 -6 + -122t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -122t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -61t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -61t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + -61t + 8t2 = 0 Solving -3 + -61t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -7.625t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -7.625t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -7.625t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -7.625t + t2 = 0 + 0.375 -7.625t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -7.625t + t2 = 0.375 The t term is -7.625t. Take half its coefficient (-3.8125). Square it (14.53515625) and add it to both sides. Add '14.53515625' to each side of the equation. -7.625t + 14.53515625 + t2 = 0.375 + 14.53515625 Reorder the terms: 14.53515625 + -7.625t + t2 = 0.375 + 14.53515625 Combine like terms: 0.375 + 14.53515625 = 14.91015625 14.53515625 + -7.625t + t2 = 14.91015625 Factor a perfect square on the left side: (t + -3.8125)(t + -3.8125) = 14.91015625 Calculate the square root of the right side: 3.861367148 Break this problem into two subproblems by setting (t + -3.8125) equal to 3.861367148 and -3.861367148.Subproblem 1
t + -3.8125 = 3.861367148 Simplifying t + -3.8125 = 3.861367148 Reorder the terms: -3.8125 + t = 3.861367148 Solving -3.8125 + t = 3.861367148 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = 3.861367148 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = 3.861367148 + 3.8125 t = 3.861367148 + 3.8125 Combine like terms: 3.861367148 + 3.8125 = 7.673867148 t = 7.673867148 Simplifying t = 7.673867148Subproblem 2
t + -3.8125 = -3.861367148 Simplifying t + -3.8125 = -3.861367148 Reorder the terms: -3.8125 + t = -3.861367148 Solving -3.8125 + t = -3.861367148 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = -3.861367148 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = -3.861367148 + 3.8125 t = -3.861367148 + 3.8125 Combine like terms: -3.861367148 + 3.8125 = -0.048867148 t = -0.048867148 Simplifying t = -0.048867148Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.673867148, -0.048867148}Solution
t = {7.673867148, -0.048867148}
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