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Simplifying 0 = -16t2 + 64t + 12 Reorder the terms: 0 = 12 + 64t + -16t2 Solving 0 = 12 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -64t + 16t2 = 12 + 64t + -16t2 + -12 + -64t + 16t2 Reorder the terms: -12 + -64t + 16t2 = 12 + -12 + 64t + -64t + -16t2 + 16t2 Combine like terms: 12 + -12 = 0 -12 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -12 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -12 + -64t + 16t2 = 0 + -16t2 + 16t2 -12 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -12 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -16t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -16t + 4t2)' equal to zero and attempt to solve: Simplifying -3 + -16t + 4t2 = 0 Solving -3 + -16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -4t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -4t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -4t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -4t + t2 = 0 + 0.75 -4t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -4t + t2 = 0.75 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 0.75 + 4 Reorder the terms: 4 + -4t + t2 = 0.75 + 4 Combine like terms: 0.75 + 4 = 4.75 4 + -4t + t2 = 4.75 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (t + -2) equal to 2.179449472 and -2.179449472.Subproblem 1
t + -2 = 2.179449472 Simplifying t + -2 = 2.179449472 Reorder the terms: -2 + t = 2.179449472 Solving -2 + t = 2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.179449472 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.179449472 + 2 t = 2.179449472 + 2 Combine like terms: 2.179449472 + 2 = 4.179449472 t = 4.179449472 Simplifying t = 4.179449472Subproblem 2
t + -2 = -2.179449472 Simplifying t + -2 = -2.179449472 Reorder the terms: -2 + t = -2.179449472 Solving -2 + t = -2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.179449472 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.179449472 + 2 t = -2.179449472 + 2 Combine like terms: -2.179449472 + 2 = -0.179449472 t = -0.179449472 Simplifying t = -0.179449472Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.179449472, -0.179449472}Solution
t = {4.179449472, -0.179449472}
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