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Simplifying 3t2 + 3t + -42 = 0 Reorder the terms: -42 + 3t + 3t2 = 0 Solving -42 + 3t + 3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-14 + t + t2)' equal to zero and attempt to solve: Simplifying -14 + t + t2 = 0 Solving -14 + t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + t + t2 = 0 + 14 t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 t + t2 = 14 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. t + 0.25 + t2 = 14 + 0.25 Reorder the terms: 0.25 + t + t2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + t + t2 = 14.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (t + 0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
t + 0.5 = 3.774917218 Simplifying t + 0.5 = 3.774917218 Reorder the terms: 0.5 + t = 3.774917218 Solving 0.5 + t = 3.774917218 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 3.774917218 + -0.5 t = 3.774917218 + -0.5 Combine like terms: 3.774917218 + -0.5 = 3.274917218 t = 3.274917218 Simplifying t = 3.274917218Subproblem 2
t + 0.5 = -3.774917218 Simplifying t + 0.5 = -3.774917218 Reorder the terms: 0.5 + t = -3.774917218 Solving 0.5 + t = -3.774917218 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -3.774917218 + -0.5 t = -3.774917218 + -0.5 Combine like terms: -3.774917218 + -0.5 = -4.274917218 t = -4.274917218 Simplifying t = -4.274917218Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.274917218, -4.274917218}Solution
t = {3.274917218, -4.274917218}
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