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Simplifying -72t2 + 45t + 15 = 0 Reorder the terms: 15 + 45t + -72t2 = 0 Solving 15 + 45t + -72t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 15t + -24t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 15t + -24t2)' equal to zero and attempt to solve: Simplifying 5 + 15t + -24t2 = 0 Solving 5 + 15t + -24t2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -0.2083333333 + -0.625t + t2 = 0 Move the constant term to the right: Add '0.2083333333' to each side of the equation. -0.2083333333 + -0.625t + 0.2083333333 + t2 = 0 + 0.2083333333 Reorder the terms: -0.2083333333 + 0.2083333333 + -0.625t + t2 = 0 + 0.2083333333 Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000 0.0000000000 + -0.625t + t2 = 0 + 0.2083333333 -0.625t + t2 = 0 + 0.2083333333 Combine like terms: 0 + 0.2083333333 = 0.2083333333 -0.625t + t2 = 0.2083333333 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 = 0.2083333333 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 0.2083333333 + 0.09765625 Combine like terms: 0.2083333333 + 0.09765625 = 0.3059895833 0.09765625 + -0.625t + t2 = 0.3059895833 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 0.3059895833 Calculate the square root of the right side: 0.553163252 Break this problem into two subproblems by setting (t + -0.3125) equal to 0.553163252 and -0.553163252.Subproblem 1
t + -0.3125 = 0.553163252 Simplifying t + -0.3125 = 0.553163252 Reorder the terms: -0.3125 + t = 0.553163252 Solving -0.3125 + t = 0.553163252 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 = 0.553163252 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 0.553163252 + 0.3125 t = 0.553163252 + 0.3125 Combine like terms: 0.553163252 + 0.3125 = 0.865663252 t = 0.865663252 Simplifying t = 0.865663252Subproblem 2
t + -0.3125 = -0.553163252 Simplifying t + -0.3125 = -0.553163252 Reorder the terms: -0.3125 + t = -0.553163252 Solving -0.3125 + t = -0.553163252 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 = -0.553163252 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -0.553163252 + 0.3125 t = -0.553163252 + 0.3125 Combine like terms: -0.553163252 + 0.3125 = -0.240663252 t = -0.240663252 Simplifying t = -0.240663252Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.865663252, -0.240663252}Solution
t = {0.865663252, -0.240663252}
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