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Simplifying 0 = -16t2 + 48t + 100 Reorder the terms: 0 = 100 + 48t + -16t2 Solving 0 = 100 + 48t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -48t + 16t2 = 100 + 48t + -16t2 + -100 + -48t + 16t2 Reorder the terms: -100 + -48t + 16t2 = 100 + -100 + 48t + -48t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 -100 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -100 + -48t + 16t2 = 0 + -16t2 + 16t2 -100 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -12t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -12t + 4t2)' equal to zero and attempt to solve: Simplifying -25 + -12t + 4t2 = 0 Solving -25 + -12t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -3t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -3t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -3t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -3t + t2 = 0 + 6.25 -3t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -3t + t2 = 6.25 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 = 6.25 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 6.25 + 2.25 Combine like terms: 6.25 + 2.25 = 8.5 2.25 + -3t + t2 = 8.5 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (t + -1.5) equal to 2.915475947 and -2.915475947.Subproblem 1
t + -1.5 = 2.915475947 Simplifying t + -1.5 = 2.915475947 Reorder the terms: -1.5 + t = 2.915475947 Solving -1.5 + t = 2.915475947 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 = 2.915475947 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 2.915475947 + 1.5 t = 2.915475947 + 1.5 Combine like terms: 2.915475947 + 1.5 = 4.415475947 t = 4.415475947 Simplifying t = 4.415475947Subproblem 2
t + -1.5 = -2.915475947 Simplifying t + -1.5 = -2.915475947 Reorder the terms: -1.5 + t = -2.915475947 Solving -1.5 + t = -2.915475947 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 = -2.915475947 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -2.915475947 + 1.5 t = -2.915475947 + 1.5 Combine like terms: -2.915475947 + 1.5 = -1.415475947 t = -1.415475947 Simplifying t = -1.415475947Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.415475947, -1.415475947}Solution
t = {4.415475947, -1.415475947}
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