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Simplifying 3t2 + -24t + 30 = 0 Reorder the terms: 30 + -24t + 3t2 = 0 Solving 30 + -24t + 3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -8t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -8t + t2)' equal to zero and attempt to solve: Simplifying 10 + -8t + t2 = 0 Solving 10 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + -8t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8t + t2 = 0 + -10 -8t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8t + t2 = -10 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -10 + 16 Reorder the terms: 16 + -8t + t2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8t + t2 = 6 Factor a perfect square on the left side: (t + -4)(t + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (t + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
t + -4 = 2.449489743 Simplifying t + -4 = 2.449489743 Reorder the terms: -4 + t = 2.449489743 Solving -4 + t = 2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + t = 2.449489743 + 4 t = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 t = 6.449489743 Simplifying t = 6.449489743Subproblem 2
t + -4 = -2.449489743 Simplifying t + -4 = -2.449489743 Reorder the terms: -4 + t = -2.449489743 Solving -4 + t = -2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + t = -2.449489743 + 4 t = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 t = 1.550510257 Simplifying t = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.449489743, 1.550510257}Solution
t = {6.449489743, 1.550510257}
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