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Simplifying 0 = -16t2 + 4t + 450 Reorder the terms: 0 = 450 + 4t + -16t2 Solving 0 = 450 + 4t + -16t2 Solving for variable 't'. Combine like terms: 0 + -450 = -450 -450 + -4t + 16t2 = 450 + 4t + -16t2 + -450 + -4t + 16t2 Reorder the terms: -450 + -4t + 16t2 = 450 + -450 + 4t + -4t + -16t2 + 16t2 Combine like terms: 450 + -450 = 0 -450 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -450 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -450 + -4t + 16t2 = 0 + -16t2 + 16t2 -450 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -450 + -4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + -2t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + -2t + 8t2)' equal to zero and attempt to solve: Simplifying -225 + -2t + 8t2 = 0 Solving -225 + -2t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -28.125 + -0.25t + t2 = 0 Move the constant term to the right: Add '28.125' to each side of the equation. -28.125 + -0.25t + 28.125 + t2 = 0 + 28.125 Reorder the terms: -28.125 + 28.125 + -0.25t + t2 = 0 + 28.125 Combine like terms: -28.125 + 28.125 = 0.000 0.000 + -0.25t + t2 = 0 + 28.125 -0.25t + t2 = 0 + 28.125 Combine like terms: 0 + 28.125 = 28.125 -0.25t + t2 = 28.125 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 28.125 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 28.125 + 0.015625 Combine like terms: 28.125 + 0.015625 = 28.140625 0.015625 + -0.25t + t2 = 28.140625 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 28.140625 Calculate the square root of the right side: 5.304773793 Break this problem into two subproblems by setting (t + -0.125) equal to 5.304773793 and -5.304773793.Subproblem 1
t + -0.125 = 5.304773793 Simplifying t + -0.125 = 5.304773793 Reorder the terms: -0.125 + t = 5.304773793 Solving -0.125 + t = 5.304773793 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 5.304773793 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 5.304773793 + 0.125 t = 5.304773793 + 0.125 Combine like terms: 5.304773793 + 0.125 = 5.429773793 t = 5.429773793 Simplifying t = 5.429773793Subproblem 2
t + -0.125 = -5.304773793 Simplifying t + -0.125 = -5.304773793 Reorder the terms: -0.125 + t = -5.304773793 Solving -0.125 + t = -5.304773793 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -5.304773793 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -5.304773793 + 0.125 t = -5.304773793 + 0.125 Combine like terms: -5.304773793 + 0.125 = -5.179773793 t = -5.179773793 Simplifying t = -5.179773793Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.429773793, -5.179773793}Solution
t = {5.429773793, -5.179773793}
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