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Simplifying 168 = 10t + 4t2 Solving 168 = 10t + 4t2 Solving for variable 't'. Reorder the terms: 168 + -10t + -4t2 = 10t + -10t + 4t2 + -4t2 Combine like terms: 10t + -10t = 0 168 + -10t + -4t2 = 0 + 4t2 + -4t2 168 + -10t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 168 + -10t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(84 + -5t + -2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(84 + -5t + -2t2)' equal to zero and attempt to solve: Simplifying 84 + -5t + -2t2 = 0 Solving 84 + -5t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -42 + 2.5t + t2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 2.5t + 42 + t2 = 0 + 42 Reorder the terms: -42 + 42 + 2.5t + t2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 2.5t + t2 = 0 + 42 2.5t + t2 = 0 + 42 Combine like terms: 0 + 42 = 42 2.5t + t2 = 42 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 42 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 42 + 1.5625 Combine like terms: 42 + 1.5625 = 43.5625 1.5625 + 2.5t + t2 = 43.5625 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 43.5625 Calculate the square root of the right side: 6.600189391 Break this problem into two subproblems by setting (t + 1.25) equal to 6.600189391 and -6.600189391.Subproblem 1
t + 1.25 = 6.600189391 Simplifying t + 1.25 = 6.600189391 Reorder the terms: 1.25 + t = 6.600189391 Solving 1.25 + t = 6.600189391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 6.600189391 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 6.600189391 + -1.25 t = 6.600189391 + -1.25 Combine like terms: 6.600189391 + -1.25 = 5.350189391 t = 5.350189391 Simplifying t = 5.350189391Subproblem 2
t + 1.25 = -6.600189391 Simplifying t + 1.25 = -6.600189391 Reorder the terms: 1.25 + t = -6.600189391 Solving 1.25 + t = -6.600189391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -6.600189391 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -6.600189391 + -1.25 t = -6.600189391 + -1.25 Combine like terms: -6.600189391 + -1.25 = -7.850189391 t = -7.850189391 Simplifying t = -7.850189391Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.350189391, -7.850189391}Solution
t = {5.350189391, -7.850189391}
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