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Simplifying 0 = -16t2 + 4t + 48 Reorder the terms: 0 = 48 + 4t + -16t2 Solving 0 = 48 + 4t + -16t2 Solving for variable 't'. Combine like terms: 0 + -48 = -48 -48 + -4t + 16t2 = 48 + 4t + -16t2 + -48 + -4t + 16t2 Reorder the terms: -48 + -4t + 16t2 = 48 + -48 + 4t + -4t + -16t2 + 16t2 Combine like terms: 48 + -48 = 0 -48 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -48 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -48 + -4t + 16t2 = 0 + -16t2 + 16t2 -48 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -48 + -4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -1t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + -1t + 4t2)' equal to zero and attempt to solve: Simplifying -12 + -1t + 4t2 = 0 Solving -12 + -1t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + -0.25t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.25t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -0.25t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.25t + t2 = 0 + 3 -0.25t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.25t + t2 = 3 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 3 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 3 + 0.015625 Combine like terms: 3 + 0.015625 = 3.015625 0.015625 + -0.25t + t2 = 3.015625 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (t + -0.125) equal to 1.736555499 and -1.736555499.Subproblem 1
t + -0.125 = 1.736555499 Simplifying t + -0.125 = 1.736555499 Reorder the terms: -0.125 + t = 1.736555499 Solving -0.125 + t = 1.736555499 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 1.736555499 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 1.736555499 + 0.125 t = 1.736555499 + 0.125 Combine like terms: 1.736555499 + 0.125 = 1.861555499 t = 1.861555499 Simplifying t = 1.861555499Subproblem 2
t + -0.125 = -1.736555499 Simplifying t + -0.125 = -1.736555499 Reorder the terms: -0.125 + t = -1.736555499 Solving -0.125 + t = -1.736555499 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -1.736555499 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -1.736555499 + 0.125 t = -1.736555499 + 0.125 Combine like terms: -1.736555499 + 0.125 = -1.611555499 t = -1.611555499 Simplifying t = -1.611555499Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.861555499, -1.611555499}Solution
t = {1.861555499, -1.611555499}
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