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Simplifying 0 = -1(3t2 + -48t + -12) Reorder the terms: 0 = -1(-12 + -48t + 3t2) 0 = (-12 * -1 + -48t * -1 + 3t2 * -1) 0 = (12 + 48t + -3t2) Solving 0 = 12 + 48t + -3t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -48t + 3t2 = 12 + 48t + -3t2 + -12 + -48t + 3t2 Reorder the terms: -12 + -48t + 3t2 = 12 + -12 + 48t + -48t + -3t2 + 3t2 Combine like terms: 12 + -12 = 0 -12 + -48t + 3t2 = 0 + 48t + -48t + -3t2 + 3t2 -12 + -48t + 3t2 = 48t + -48t + -3t2 + 3t2 Combine like terms: 48t + -48t = 0 -12 + -48t + 3t2 = 0 + -3t2 + 3t2 -12 + -48t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 -12 + -48t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -16t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -16t + t2)' equal to zero and attempt to solve: Simplifying -4 + -16t + t2 = 0 Solving -4 + -16t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -16t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -16t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -16t + t2 = 0 + 4 -16t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -16t + t2 = 4 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = 4 + 64 Reorder the terms: 64 + -16t + t2 = 4 + 64 Combine like terms: 4 + 64 = 68 64 + -16t + t2 = 68 Factor a perfect square on the left side: (t + -8)(t + -8) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (t + -8) equal to 8.246211251 and -8.246211251.Subproblem 1
t + -8 = 8.246211251 Simplifying t + -8 = 8.246211251 Reorder the terms: -8 + t = 8.246211251 Solving -8 + t = 8.246211251 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 8.246211251 + 8 Combine like terms: -8 + 8 = 0 0 + t = 8.246211251 + 8 t = 8.246211251 + 8 Combine like terms: 8.246211251 + 8 = 16.246211251 t = 16.246211251 Simplifying t = 16.246211251Subproblem 2
t + -8 = -8.246211251 Simplifying t + -8 = -8.246211251 Reorder the terms: -8 + t = -8.246211251 Solving -8 + t = -8.246211251 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -8.246211251 + 8 Combine like terms: -8 + 8 = 0 0 + t = -8.246211251 + 8 t = -8.246211251 + 8 Combine like terms: -8.246211251 + 8 = -0.246211251 t = -0.246211251 Simplifying t = -0.246211251Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.246211251, -0.246211251}Solution
t = {16.246211251, -0.246211251}
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