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Simplifying 0 = -16t2 + 74t + 240 Reorder the terms: 0 = 240 + 74t + -16t2 Solving 0 = 240 + 74t + -16t2 Solving for variable 't'. Combine like terms: 0 + -240 = -240 -240 + -74t + 16t2 = 240 + 74t + -16t2 + -240 + -74t + 16t2 Reorder the terms: -240 + -74t + 16t2 = 240 + -240 + 74t + -74t + -16t2 + 16t2 Combine like terms: 240 + -240 = 0 -240 + -74t + 16t2 = 0 + 74t + -74t + -16t2 + 16t2 -240 + -74t + 16t2 = 74t + -74t + -16t2 + 16t2 Combine like terms: 74t + -74t = 0 -240 + -74t + 16t2 = 0 + -16t2 + 16t2 -240 + -74t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -240 + -74t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-120 + -37t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-120 + -37t + 8t2)' equal to zero and attempt to solve: Simplifying -120 + -37t + 8t2 = 0 Solving -120 + -37t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15 + -4.625t + t2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -4.625t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + -4.625t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4.625t + t2 = 0 + 15 -4.625t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4.625t + t2 = 15 The t term is -4.625t. Take half its coefficient (-2.3125). Square it (5.34765625) and add it to both sides. Add '5.34765625' to each side of the equation. -4.625t + 5.34765625 + t2 = 15 + 5.34765625 Reorder the terms: 5.34765625 + -4.625t + t2 = 15 + 5.34765625 Combine like terms: 15 + 5.34765625 = 20.34765625 5.34765625 + -4.625t + t2 = 20.34765625 Factor a perfect square on the left side: (t + -2.3125)(t + -2.3125) = 20.34765625 Calculate the square root of the right side: 4.510837644 Break this problem into two subproblems by setting (t + -2.3125) equal to 4.510837644 and -4.510837644.Subproblem 1
t + -2.3125 = 4.510837644 Simplifying t + -2.3125 = 4.510837644 Reorder the terms: -2.3125 + t = 4.510837644 Solving -2.3125 + t = 4.510837644 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.3125' to each side of the equation. -2.3125 + 2.3125 + t = 4.510837644 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + t = 4.510837644 + 2.3125 t = 4.510837644 + 2.3125 Combine like terms: 4.510837644 + 2.3125 = 6.823337644 t = 6.823337644 Simplifying t = 6.823337644Subproblem 2
t + -2.3125 = -4.510837644 Simplifying t + -2.3125 = -4.510837644 Reorder the terms: -2.3125 + t = -4.510837644 Solving -2.3125 + t = -4.510837644 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.3125' to each side of the equation. -2.3125 + 2.3125 + t = -4.510837644 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + t = -4.510837644 + 2.3125 t = -4.510837644 + 2.3125 Combine like terms: -4.510837644 + 2.3125 = -2.198337644 t = -2.198337644 Simplifying t = -2.198337644Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.823337644, -2.198337644}Solution
t = {6.823337644, -2.198337644}
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