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Simplifying 0 = 16t2 + 35t + 2 Reorder the terms: 0 = 2 + 35t + 16t2 Solving 0 = 2 + 35t + 16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -35t + -16t2 = 2 + 35t + 16t2 + -2 + -35t + -16t2 Reorder the terms: -2 + -35t + -16t2 = 2 + -2 + 35t + -35t + 16t2 + -16t2 Combine like terms: 2 + -2 = 0 -2 + -35t + -16t2 = 0 + 35t + -35t + 16t2 + -16t2 -2 + -35t + -16t2 = 35t + -35t + 16t2 + -16t2 Combine like terms: 35t + -35t = 0 -2 + -35t + -16t2 = 0 + 16t2 + -16t2 -2 + -35t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -2 + -35t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 35t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 35t + 16t2)' equal to zero and attempt to solve: Simplifying 2 + 35t + 16t2 = 0 Solving 2 + 35t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.125 + 2.1875t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 2.1875t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 2.1875t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 2.1875t + t2 = 0 + -0.125 2.1875t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 2.1875t + t2 = -0.125 The t term is 2.1875t. Take half its coefficient (1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. 2.1875t + 1.196289063 + t2 = -0.125 + 1.196289063 Reorder the terms: 1.196289063 + 2.1875t + t2 = -0.125 + 1.196289063 Combine like terms: -0.125 + 1.196289063 = 1.071289063 1.196289063 + 2.1875t + t2 = 1.071289063 Factor a perfect square on the left side: (t + 1.09375)(t + 1.09375) = 1.071289063 Calculate the square root of the right side: 1.035030948 Break this problem into two subproblems by setting (t + 1.09375) equal to 1.035030948 and -1.035030948.Subproblem 1
t + 1.09375 = 1.035030948 Simplifying t + 1.09375 = 1.035030948 Reorder the terms: 1.09375 + t = 1.035030948 Solving 1.09375 + t = 1.035030948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + t = 1.035030948 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + t = 1.035030948 + -1.09375 t = 1.035030948 + -1.09375 Combine like terms: 1.035030948 + -1.09375 = -0.058719052 t = -0.058719052 Simplifying t = -0.058719052Subproblem 2
t + 1.09375 = -1.035030948 Simplifying t + 1.09375 = -1.035030948 Reorder the terms: 1.09375 + t = -1.035030948 Solving 1.09375 + t = -1.035030948 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + t = -1.035030948 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + t = -1.035030948 + -1.09375 t = -1.035030948 + -1.09375 Combine like terms: -1.035030948 + -1.09375 = -2.128780948 t = -2.128780948 Simplifying t = -2.128780948Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.058719052, -2.128780948}Solution
t = {-0.058719052, -2.128780948}
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