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Simplifying 16t2 + 90t = 126 Reorder the terms: 90t + 16t2 = 126 Solving 90t + 16t2 = 126 Solving for variable 't'. Reorder the terms: -126 + 90t + 16t2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 90t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-63 + 45t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-63 + 45t + 8t2)' equal to zero and attempt to solve: Simplifying -63 + 45t + 8t2 = 0 Solving -63 + 45t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7.875 + 5.625t + t2 = 0 Move the constant term to the right: Add '7.875' to each side of the equation. -7.875 + 5.625t + 7.875 + t2 = 0 + 7.875 Reorder the terms: -7.875 + 7.875 + 5.625t + t2 = 0 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + 5.625t + t2 = 0 + 7.875 5.625t + t2 = 0 + 7.875 Combine like terms: 0 + 7.875 = 7.875 5.625t + t2 = 7.875 The t term is 5.625t. Take half its coefficient (2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. 5.625t + 7.91015625 + t2 = 7.875 + 7.91015625 Reorder the terms: 7.91015625 + 5.625t + t2 = 7.875 + 7.91015625 Combine like terms: 7.875 + 7.91015625 = 15.78515625 7.91015625 + 5.625t + t2 = 15.78515625 Factor a perfect square on the left side: (t + 2.8125)(t + 2.8125) = 15.78515625 Calculate the square root of the right side: 3.973053769 Break this problem into two subproblems by setting (t + 2.8125) equal to 3.973053769 and -3.973053769.Subproblem 1
t + 2.8125 = 3.973053769 Simplifying t + 2.8125 = 3.973053769 Reorder the terms: 2.8125 + t = 3.973053769 Solving 2.8125 + t = 3.973053769 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.8125' to each side of the equation. 2.8125 + -2.8125 + t = 3.973053769 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + t = 3.973053769 + -2.8125 t = 3.973053769 + -2.8125 Combine like terms: 3.973053769 + -2.8125 = 1.160553769 t = 1.160553769 Simplifying t = 1.160553769Subproblem 2
t + 2.8125 = -3.973053769 Simplifying t + 2.8125 = -3.973053769 Reorder the terms: 2.8125 + t = -3.973053769 Solving 2.8125 + t = -3.973053769 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.8125' to each side of the equation. 2.8125 + -2.8125 + t = -3.973053769 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + t = -3.973053769 + -2.8125 t = -3.973053769 + -2.8125 Combine like terms: -3.973053769 + -2.8125 = -6.785553769 t = -6.785553769 Simplifying t = -6.785553769Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.160553769, -6.785553769}Solution
t = {1.160553769, -6.785553769}
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