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Simplifying 0 = -16(t2 + -15t + -5) Reorder the terms: 0 = -16(-5 + -15t + t2) 0 = (-5 * -16 + -15t * -16 + t2 * -16) 0 = (80 + 240t + -16t2) Solving 0 = 80 + 240t + -16t2 Solving for variable 't'. Combine like terms: 0 + -80 = -80 -80 + -240t + 16t2 = 80 + 240t + -16t2 + -80 + -240t + 16t2 Reorder the terms: -80 + -240t + 16t2 = 80 + -80 + 240t + -240t + -16t2 + 16t2 Combine like terms: 80 + -80 = 0 -80 + -240t + 16t2 = 0 + 240t + -240t + -16t2 + 16t2 -80 + -240t + 16t2 = 240t + -240t + -16t2 + 16t2 Combine like terms: 240t + -240t = 0 -80 + -240t + 16t2 = 0 + -16t2 + 16t2 -80 + -240t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -80 + -240t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-5 + -15t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-5 + -15t + t2)' equal to zero and attempt to solve: Simplifying -5 + -15t + t2 = 0 Solving -5 + -15t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -15t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -15t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -15t + t2 = 0 + 5 -15t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -15t + t2 = 5 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = 5 + 56.25 Reorder the terms: 56.25 + -15t + t2 = 5 + 56.25 Combine like terms: 5 + 56.25 = 61.25 56.25 + -15t + t2 = 61.25 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (t + -7.5) equal to 7.826237921 and -7.826237921.Subproblem 1
t + -7.5 = 7.826237921 Simplifying t + -7.5 = 7.826237921 Reorder the terms: -7.5 + t = 7.826237921 Solving -7.5 + t = 7.826237921 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 7.826237921 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 7.826237921 + 7.5 t = 7.826237921 + 7.5 Combine like terms: 7.826237921 + 7.5 = 15.326237921 t = 15.326237921 Simplifying t = 15.326237921Subproblem 2
t + -7.5 = -7.826237921 Simplifying t + -7.5 = -7.826237921 Reorder the terms: -7.5 + t = -7.826237921 Solving -7.5 + t = -7.826237921 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -7.826237921 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -7.826237921 + 7.5 t = -7.826237921 + 7.5 Combine like terms: -7.826237921 + 7.5 = -0.326237921 t = -0.326237921 Simplifying t = -0.326237921Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.326237921, -0.326237921}Solution
t = {15.326237921, -0.326237921}
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