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Simplifying -2(8t2 + 17t + 4) = 0 Reorder the terms: -2(4 + 17t + 8t2) = 0 (4 * -2 + 17t * -2 + 8t2 * -2) = 0 (-8 + -34t + -16t2) = 0 Solving -8 + -34t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 17t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 17t + 8t2)' equal to zero and attempt to solve: Simplifying 4 + 17t + 8t2 = 0 Solving 4 + 17t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.5 + 2.125t + t2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 2.125t + -0.5 + t2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 2.125t + t2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 2.125t + t2 = 0 + -0.5 2.125t + t2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 2.125t + t2 = -0.5 The t term is 2.125t. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125t + 1.12890625 + t2 = -0.5 + 1.12890625 Reorder the terms: 1.12890625 + 2.125t + t2 = -0.5 + 1.12890625 Combine like terms: -0.5 + 1.12890625 = 0.62890625 1.12890625 + 2.125t + t2 = 0.62890625 Factor a perfect square on the left side: (t + 1.0625)(t + 1.0625) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (t + 1.0625) equal to 0.793036096 and -0.793036096.Subproblem 1
t + 1.0625 = 0.793036096 Simplifying t + 1.0625 = 0.793036096 Reorder the terms: 1.0625 + t = 0.793036096 Solving 1.0625 + t = 0.793036096 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + t = 0.793036096 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + t = 0.793036096 + -1.0625 t = 0.793036096 + -1.0625 Combine like terms: 0.793036096 + -1.0625 = -0.269463904 t = -0.269463904 Simplifying t = -0.269463904Subproblem 2
t + 1.0625 = -0.793036096 Simplifying t + 1.0625 = -0.793036096 Reorder the terms: 1.0625 + t = -0.793036096 Solving 1.0625 + t = -0.793036096 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + t = -0.793036096 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + t = -0.793036096 + -1.0625 t = -0.793036096 + -1.0625 Combine like terms: -0.793036096 + -1.0625 = -1.855536096 t = -1.855536096 Simplifying t = -1.855536096Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.269463904, -1.855536096}Solution
t = {-0.269463904, -1.855536096}
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