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Simplifying -16t2 + 6t + 800 = 0 Reorder the terms: 800 + 6t + -16t2 = 0 Solving 800 + 6t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(400 + 3t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(400 + 3t + -8t2)' equal to zero and attempt to solve: Simplifying 400 + 3t + -8t2 = 0 Solving 400 + 3t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -50 + -0.375t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -0.375t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + -0.375t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -0.375t + t2 = 0 + 50 -0.375t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 -0.375t + t2 = 50 The t term is -0.375t. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375t + 0.03515625 + t2 = 50 + 0.03515625 Reorder the terms: 0.03515625 + -0.375t + t2 = 50 + 0.03515625 Combine like terms: 50 + 0.03515625 = 50.03515625 0.03515625 + -0.375t + t2 = 50.03515625 Factor a perfect square on the left side: (t + -0.1875)(t + -0.1875) = 50.03515625 Calculate the square root of the right side: 7.073553297 Break this problem into two subproblems by setting (t + -0.1875) equal to 7.073553297 and -7.073553297.Subproblem 1
t + -0.1875 = 7.073553297 Simplifying t + -0.1875 = 7.073553297 Reorder the terms: -0.1875 + t = 7.073553297 Solving -0.1875 + t = 7.073553297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + t = 7.073553297 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + t = 7.073553297 + 0.1875 t = 7.073553297 + 0.1875 Combine like terms: 7.073553297 + 0.1875 = 7.261053297 t = 7.261053297 Simplifying t = 7.261053297Subproblem 2
t + -0.1875 = -7.073553297 Simplifying t + -0.1875 = -7.073553297 Reorder the terms: -0.1875 + t = -7.073553297 Solving -0.1875 + t = -7.073553297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + t = -7.073553297 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + t = -7.073553297 + 0.1875 t = -7.073553297 + 0.1875 Combine like terms: -7.073553297 + 0.1875 = -6.886053297 t = -6.886053297 Simplifying t = -6.886053297Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.261053297, -6.886053297}Solution
t = {7.261053297, -6.886053297}
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