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Simplifying -16t2 + -26t + 180 = 0 Reorder the terms: 180 + -26t + -16t2 = 0 Solving 180 + -26t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -13t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -13t + -8t2)' equal to zero and attempt to solve: Simplifying 90 + -13t + -8t2 = 0 Solving 90 + -13t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -11.25 + 1.625t + t2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 1.625t + 11.25 + t2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 1.625t + t2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 1.625t + t2 = 0 + 11.25 1.625t + t2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 1.625t + t2 = 11.25 The t term is 1.625t. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625t + 0.66015625 + t2 = 11.25 + 0.66015625 Reorder the terms: 0.66015625 + 1.625t + t2 = 11.25 + 0.66015625 Combine like terms: 11.25 + 0.66015625 = 11.91015625 0.66015625 + 1.625t + t2 = 11.91015625 Factor a perfect square on the left side: (t + 0.8125)(t + 0.8125) = 11.91015625 Calculate the square root of the right side: 3.451109423 Break this problem into two subproblems by setting (t + 0.8125) equal to 3.451109423 and -3.451109423.Subproblem 1
t + 0.8125 = 3.451109423 Simplifying t + 0.8125 = 3.451109423 Reorder the terms: 0.8125 + t = 3.451109423 Solving 0.8125 + t = 3.451109423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + t = 3.451109423 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + t = 3.451109423 + -0.8125 t = 3.451109423 + -0.8125 Combine like terms: 3.451109423 + -0.8125 = 2.638609423 t = 2.638609423 Simplifying t = 2.638609423Subproblem 2
t + 0.8125 = -3.451109423 Simplifying t + 0.8125 = -3.451109423 Reorder the terms: 0.8125 + t = -3.451109423 Solving 0.8125 + t = -3.451109423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + t = -3.451109423 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + t = -3.451109423 + -0.8125 t = -3.451109423 + -0.8125 Combine like terms: -3.451109423 + -0.8125 = -4.263609423 t = -4.263609423 Simplifying t = -4.263609423Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.638609423, -4.263609423}Solution
t = {2.638609423, -4.263609423}
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