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Simplifying -8t2 + 28t + 64 = 0 Reorder the terms: 64 + 28t + -8t2 = 0 Solving 64 + 28t + -8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + 7t + -2t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(16 + 7t + -2t2)' equal to zero and attempt to solve: Simplifying 16 + 7t + -2t2 = 0 Solving 16 + 7t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8 + -3.5t + t2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -3.5t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + -3.5t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3.5t + t2 = 0 + 8 -3.5t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3.5t + t2 = 8 The t term is -3.5t. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5t + 3.0625 + t2 = 8 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = 8 + 3.0625 Combine like terms: 8 + 3.0625 = 11.0625 3.0625 + -3.5t + t2 = 11.0625 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (t + -1.75) equal to 3.326033674 and -3.326033674.Subproblem 1
t + -1.75 = 3.326033674 Simplifying t + -1.75 = 3.326033674 Reorder the terms: -1.75 + t = 3.326033674 Solving -1.75 + t = 3.326033674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = 3.326033674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 3.326033674 + 1.75 t = 3.326033674 + 1.75 Combine like terms: 3.326033674 + 1.75 = 5.076033674 t = 5.076033674 Simplifying t = 5.076033674Subproblem 2
t + -1.75 = -3.326033674 Simplifying t + -1.75 = -3.326033674 Reorder the terms: -1.75 + t = -3.326033674 Solving -1.75 + t = -3.326033674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = -3.326033674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -3.326033674 + 1.75 t = -3.326033674 + 1.75 Combine like terms: -3.326033674 + 1.75 = -1.576033674 t = -1.576033674 Simplifying t = -1.576033674Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.076033674, -1.576033674}Solution
t = {5.076033674, -1.576033674}
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