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Simplifying -16t2 + -26t + 130 = 0 Reorder the terms: 130 + -26t + -16t2 = 0 Solving 130 + -26t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(65 + -13t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(65 + -13t + -8t2)' equal to zero and attempt to solve: Simplifying 65 + -13t + -8t2 = 0 Solving 65 + -13t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -8.125 + 1.625t + t2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + 1.625t + 8.125 + t2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + 1.625t + t2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + 1.625t + t2 = 0 + 8.125 1.625t + t2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 1.625t + t2 = 8.125 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 = 8.125 + 0.66015625 Reorder the terms: 0.66015625 + 1.625t + t2 = 8.125 + 0.66015625 Combine like terms: 8.125 + 0.66015625 = 8.78515625 0.66015625 + 1.625t + t2 = 8.78515625 Factor a perfect square on the left side: (t + 0.8125)(t + 0.8125) = 8.78515625 Calculate the square root of the right side: 2.963976425 Break this problem into two subproblems by setting (t + 0.8125) equal to 2.963976425 and -2.963976425.Subproblem 1
t + 0.8125 = 2.963976425 Simplifying t + 0.8125 = 2.963976425 Reorder the terms: 0.8125 + t = 2.963976425 Solving 0.8125 + t = 2.963976425 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 = 2.963976425 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + t = 2.963976425 + -0.8125 t = 2.963976425 + -0.8125 Combine like terms: 2.963976425 + -0.8125 = 2.151476425 t = 2.151476425 Simplifying t = 2.151476425Subproblem 2
t + 0.8125 = -2.963976425 Simplifying t + 0.8125 = -2.963976425 Reorder the terms: 0.8125 + t = -2.963976425 Solving 0.8125 + t = -2.963976425 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 = -2.963976425 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + t = -2.963976425 + -0.8125 t = -2.963976425 + -0.8125 Combine like terms: -2.963976425 + -0.8125 = -3.776476425 t = -3.776476425 Simplifying t = -3.776476425Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.151476425, -3.776476425}Solution
t = {2.151476425, -3.776476425}
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