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Simplifying 28t2 + -8t = 4 Reorder the terms: -8t + 28t2 = 4 Solving -8t + 28t2 = 4 Solving for variable 't'. Reorder the terms: -4 + -8t + 28t2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -8t + 28t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -2t + 7t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2t + 7t2)' equal to zero and attempt to solve: Simplifying -1 + -2t + 7t2 = 0 Solving -1 + -2t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.2857142857t + t2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.2857142857t + 0.1428571429 + t2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.2857142857t + t2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857t + t2 = 0 + 0.1428571429 -0.2857142857t + t2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.2857142857t + t2 = 0.1428571429 The t term is -0.2857142857t. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857t + 0.02040816328 + t2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857t + t2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + -0.2857142857t + t2 = 0.16326530618 Factor a perfect square on the left side: (t + -0.1428571429)(t + -0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (t + -0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
t + -0.1428571429 = 0.404061018 Simplifying t + -0.1428571429 = 0.404061018 Reorder the terms: -0.1428571429 + t = 0.404061018 Solving -0.1428571429 + t = 0.404061018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + t = 0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + t = 0.404061018 + 0.1428571429 t = 0.404061018 + 0.1428571429 Combine like terms: 0.404061018 + 0.1428571429 = 0.5469181609 t = 0.5469181609 Simplifying t = 0.5469181609Subproblem 2
t + -0.1428571429 = -0.404061018 Simplifying t + -0.1428571429 = -0.404061018 Reorder the terms: -0.1428571429 + t = -0.404061018 Solving -0.1428571429 + t = -0.404061018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + t = -0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + t = -0.404061018 + 0.1428571429 t = -0.404061018 + 0.1428571429 Combine like terms: -0.404061018 + 0.1428571429 = -0.2612038751 t = -0.2612038751 Simplifying t = -0.2612038751Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.5469181609, -0.2612038751}Solution
t = {0.5469181609, -0.2612038751}
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