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Simplifying 4t2 + 12t = 12 Reorder the terms: 12t + 4t2 = 12 Solving 12t + 4t2 = 12 Solving for variable 't'. Reorder the terms: -12 + 12t + 4t2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 12t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 3t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 3t + t2)' equal to zero and attempt to solve: Simplifying -3 + 3t + t2 = 0 Solving -3 + 3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 3t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 3t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3t + t2 = 0 + 3 3t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 3t + t2 = 3 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 = 3 + 2.25 Reorder the terms: 2.25 + 3t + t2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + 3t + t2 = 5.25 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (t + 1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
t + 1.5 = 2.291287847 Simplifying t + 1.5 = 2.291287847 Reorder the terms: 1.5 + t = 2.291287847 Solving 1.5 + t = 2.291287847 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 = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 2.291287847 + -1.5 t = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 t = 0.791287847 Simplifying t = 0.791287847Subproblem 2
t + 1.5 = -2.291287847 Simplifying t + 1.5 = -2.291287847 Reorder the terms: 1.5 + t = -2.291287847 Solving 1.5 + t = -2.291287847 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 = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -2.291287847 + -1.5 t = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 t = -3.791287847 Simplifying t = -3.791287847Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.791287847, -3.791287847}Solution
t = {0.791287847, -3.791287847}
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