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Simplifying -16t2 + -50t + 300 = 0 Reorder the terms: 300 + -50t + -16t2 = 0 Solving 300 + -50t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(150 + -25t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(150 + -25t + -8t2)' equal to zero and attempt to solve: Simplifying 150 + -25t + -8t2 = 0 Solving 150 + -25t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -18.75 + 3.125t + t2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 3.125t + 18.75 + t2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 3.125t + t2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 3.125t + t2 = 0 + 18.75 3.125t + t2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 3.125t + t2 = 18.75 The t term is 3.125t. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125t + 2.44140625 + t2 = 18.75 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = 18.75 + 2.44140625 Combine like terms: 18.75 + 2.44140625 = 21.19140625 2.44140625 + 3.125t + t2 = 21.19140625 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = 21.19140625 Calculate the square root of the right side: 4.603412457 Break this problem into two subproblems by setting (t + 1.5625) equal to 4.603412457 and -4.603412457.Subproblem 1
t + 1.5625 = 4.603412457 Simplifying t + 1.5625 = 4.603412457 Reorder the terms: 1.5625 + t = 4.603412457 Solving 1.5625 + t = 4.603412457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = 4.603412457 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = 4.603412457 + -1.5625 t = 4.603412457 + -1.5625 Combine like terms: 4.603412457 + -1.5625 = 3.040912457 t = 3.040912457 Simplifying t = 3.040912457Subproblem 2
t + 1.5625 = -4.603412457 Simplifying t + 1.5625 = -4.603412457 Reorder the terms: 1.5625 + t = -4.603412457 Solving 1.5625 + t = -4.603412457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = -4.603412457 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = -4.603412457 + -1.5625 t = -4.603412457 + -1.5625 Combine like terms: -4.603412457 + -1.5625 = -6.165912457 t = -6.165912457 Simplifying t = -6.165912457Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.040912457, -6.165912457}Solution
t = {3.040912457, -6.165912457}
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