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Simplifying -16t2 + 48t + 10 = 0 Reorder the terms: 10 + 48t + -16t2 = 0 Solving 10 + 48t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 24t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 24t + -8t2)' equal to zero and attempt to solve: Simplifying 5 + 24t + -8t2 = 0 Solving 5 + 24t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -3t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -3t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -3t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -3t + t2 = 0 + 0.625 -3t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -3t + t2 = 0.625 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 0.625 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 0.625 + 2.25 Combine like terms: 0.625 + 2.25 = 2.875 2.25 + -3t + t2 = 2.875 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (t + -1.5) equal to 1.695582496 and -1.695582496.Subproblem 1
t + -1.5 = 1.695582496 Simplifying t + -1.5 = 1.695582496 Reorder the terms: -1.5 + t = 1.695582496 Solving -1.5 + t = 1.695582496 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 1.695582496 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.695582496 + 1.5 t = 1.695582496 + 1.5 Combine like terms: 1.695582496 + 1.5 = 3.195582496 t = 3.195582496 Simplifying t = 3.195582496Subproblem 2
t + -1.5 = -1.695582496 Simplifying t + -1.5 = -1.695582496 Reorder the terms: -1.5 + t = -1.695582496 Solving -1.5 + t = -1.695582496 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -1.695582496 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.695582496 + 1.5 t = -1.695582496 + 1.5 Combine like terms: -1.695582496 + 1.5 = -0.195582496 t = -0.195582496 Simplifying t = -0.195582496Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.195582496, -0.195582496}Solution
t = {3.195582496, -0.195582496}
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