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Simplifying 16t2 + 10t + -12 = 0 Reorder the terms: -12 + 10t + 16t2 = 0 Solving -12 + 10t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying -6 + 5t + 8t2 = 0 Solving -6 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + 0.625t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.625t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.625t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.625t + t2 = 0 + 0.75 0.625t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.625t + t2 = 0.75 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 0.75 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 0.75 + 0.09765625 Combine like terms: 0.75 + 0.09765625 = 0.84765625 0.09765625 + 0.625t + t2 = 0.84765625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 0.84765625 Calculate the square root of the right side: 0.920682491 Break this problem into two subproblems by setting (t + 0.3125) equal to 0.920682491 and -0.920682491.Subproblem 1
t + 0.3125 = 0.920682491 Simplifying t + 0.3125 = 0.920682491 Reorder the terms: 0.3125 + t = 0.920682491 Solving 0.3125 + t = 0.920682491 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 0.920682491 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 0.920682491 + -0.3125 t = 0.920682491 + -0.3125 Combine like terms: 0.920682491 + -0.3125 = 0.608182491 t = 0.608182491 Simplifying t = 0.608182491Subproblem 2
t + 0.3125 = -0.920682491 Simplifying t + 0.3125 = -0.920682491 Reorder the terms: 0.3125 + t = -0.920682491 Solving 0.3125 + t = -0.920682491 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -0.920682491 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -0.920682491 + -0.3125 t = -0.920682491 + -0.3125 Combine like terms: -0.920682491 + -0.3125 = -1.233182491 t = -1.233182491 Simplifying t = -1.233182491Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.608182491, -1.233182491}Solution
t = {0.608182491, -1.233182491}
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