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Simplifying -16t2 + 80t + 30 = 0 Reorder the terms: 30 + 80t + -16t2 = 0 Solving 30 + 80t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 40t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 40t + -8t2)' equal to zero and attempt to solve: Simplifying 15 + 40t + -8t2 = 0 Solving 15 + 40t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + -5t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -5t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -5t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -5t + t2 = 0 + 1.875 -5t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -5t + t2 = 1.875 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 1.875 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 1.875 + 6.25 Combine like terms: 1.875 + 6.25 = 8.125 6.25 + -5t + t2 = 8.125 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 8.125 Calculate the square root of the right side: 2.850438563 Break this problem into two subproblems by setting (t + -2.5) equal to 2.850438563 and -2.850438563.Subproblem 1
t + -2.5 = 2.850438563 Simplifying t + -2.5 = 2.850438563 Reorder the terms: -2.5 + t = 2.850438563 Solving -2.5 + t = 2.850438563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.850438563 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.850438563 + 2.5 t = 2.850438563 + 2.5 Combine like terms: 2.850438563 + 2.5 = 5.350438563 t = 5.350438563 Simplifying t = 5.350438563Subproblem 2
t + -2.5 = -2.850438563 Simplifying t + -2.5 = -2.850438563 Reorder the terms: -2.5 + t = -2.850438563 Solving -2.5 + t = -2.850438563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.850438563 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.850438563 + 2.5 t = -2.850438563 + 2.5 Combine like terms: -2.850438563 + 2.5 = -0.350438563 t = -0.350438563 Simplifying t = -0.350438563Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.350438563, -0.350438563}Solution
t = {5.350438563, -0.350438563}
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