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Simplifying -16t2 + -10t + 600 = 0 Reorder the terms: 600 + -10t + -16t2 = 0 Solving 600 + -10t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(300 + -5t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(300 + -5t + -8t2)' equal to zero and attempt to solve: Simplifying 300 + -5t + -8t2 = 0 Solving 300 + -5t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -37.5 + 0.625t + t2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 0.625t + 37.5 + t2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 0.625t + t2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 0.625t + t2 = 0 + 37.5 0.625t + t2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 0.625t + t2 = 37.5 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 = 37.5 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 37.5 + 0.09765625 Combine like terms: 37.5 + 0.09765625 = 37.59765625 0.09765625 + 0.625t + t2 = 37.59765625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 37.59765625 Calculate the square root of the right side: 6.131692772 Break this problem into two subproblems by setting (t + 0.3125) equal to 6.131692772 and -6.131692772.Subproblem 1
t + 0.3125 = 6.131692772 Simplifying t + 0.3125 = 6.131692772 Reorder the terms: 0.3125 + t = 6.131692772 Solving 0.3125 + t = 6.131692772 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 = 6.131692772 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 6.131692772 + -0.3125 t = 6.131692772 + -0.3125 Combine like terms: 6.131692772 + -0.3125 = 5.819192772 t = 5.819192772 Simplifying t = 5.819192772Subproblem 2
t + 0.3125 = -6.131692772 Simplifying t + 0.3125 = -6.131692772 Reorder the terms: 0.3125 + t = -6.131692772 Solving 0.3125 + t = -6.131692772 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 = -6.131692772 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -6.131692772 + -0.3125 t = -6.131692772 + -0.3125 Combine like terms: -6.131692772 + -0.3125 = -6.444192772 t = -6.444192772 Simplifying t = -6.444192772Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.819192772, -6.444192772}Solution
t = {5.819192772, -6.444192772}
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