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Simplifying (12t2) + -1(12t) + 2 = 0 Remove parenthesis around (12t) (12t2) + -1 * 12t + 2 = 0 Multiply -1 * 12 (12t2) + -12t + 2 = 0 Reorder the terms: 2 + -12t + (12t2) = 0 Solving 2 + -12t + (12t2) = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -6t + (6t2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -6t + (6t2))' equal to zero and attempt to solve: Simplifying 1 + -6t + (6t2) = 0 Solving 1 + -6t + (6t2) = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -1t + t2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1t + -0.1666666667 + t2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1t + t2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1t + t2 = 0 + -0.1666666667 -1t + t2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1t + t2 = -0.1666666667 The t term is -1t. 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. -1t + 0.25 + t2 = -0.1666666667 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -0.1666666667 + 0.25 Combine like terms: -0.1666666667 + 0.25 = 0.0833333333 0.25 + -1t + t2 = 0.0833333333 Factor a perfect square on the left side: ((t) + -0.5)((t) + -0.5) = 0.0833333333 Calculate the square root of the right side: 0.288675135 Break this problem into two subproblems by setting ((t) + -0.5) equal to 0.288675135 and -0.288675135.Subproblem 1
(t) + -0.5 = 0.288675135 Simplifying (t) + -0.5 = 0.288675135 t + -0.5 = 0.288675135 Reorder the terms: -0.5 + t = 0.288675135 Solving -0.5 + t = 0.288675135 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 = 0.288675135 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.288675135 + 0.5 t = 0.288675135 + 0.5 Combine like terms: 0.288675135 + 0.5 = 0.788675135 t = 0.788675135 Simplifying t = 0.788675135Subproblem 2
(t) + -0.5 = -0.288675135 Simplifying (t) + -0.5 = -0.288675135 t + -0.5 = -0.288675135 Reorder the terms: -0.5 + t = -0.288675135 Solving -0.5 + t = -0.288675135 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 = -0.288675135 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.288675135 + 0.5 t = -0.288675135 + 0.5 Combine like terms: -0.288675135 + 0.5 = 0.211324865 t = 0.211324865 Simplifying t = 0.211324865Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.788675135, 0.211324865}Solution
t = {0.788675135, 0.211324865}
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