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Simplifying (-16t2) + -1(22t) + (220) = 0 Remove parenthesis around (22t) (-16t2) + -1 * 22t + (220) = 0 Multiply -1 * 22 (-16t2) + -22t + (220) = 0 (-16t2) + -22t + 220 = 0 Reorder the terms: 220 + -22t + (-16t2) = 0 Solving 220 + -22t + (-16t2) = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(110 + -11t + (-8t2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(110 + -11t + (-8t2))' equal to zero and attempt to solve: Simplifying 110 + -11t + (-8t2) = 0 Solving 110 + -11t + (-8t2) = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -13.75 + 1.375t + t2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 1.375t + 13.75 + t2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 1.375t + t2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 1.375t + t2 = 0 + 13.75 1.375t + t2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 1.375t + t2 = 13.75 The t term is 1.375t. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375t + 0.47265625 + t2 = 13.75 + 0.47265625 Reorder the terms: 0.47265625 + 1.375t + t2 = 13.75 + 0.47265625 Combine like terms: 13.75 + 0.47265625 = 14.22265625 0.47265625 + 1.375t + t2 = 14.22265625 Factor a perfect square on the left side: ((t) + 0.6875)((t) + 0.6875) = 14.22265625 Calculate the square root of the right side: 3.77129371 Break this problem into two subproblems by setting ((t) + 0.6875) equal to 3.77129371 and -3.77129371.Subproblem 1
(t) + 0.6875 = 3.77129371 Simplifying (t) + 0.6875 = 3.77129371 t + 0.6875 = 3.77129371 Reorder the terms: 0.6875 + t = 3.77129371 Solving 0.6875 + t = 3.77129371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + t = 3.77129371 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + t = 3.77129371 + -0.6875 t = 3.77129371 + -0.6875 Combine like terms: 3.77129371 + -0.6875 = 3.08379371 t = 3.08379371 Simplifying t = 3.08379371Subproblem 2
(t) + 0.6875 = -3.77129371 Simplifying (t) + 0.6875 = -3.77129371 t + 0.6875 = -3.77129371 Reorder the terms: 0.6875 + t = -3.77129371 Solving 0.6875 + t = -3.77129371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + t = -3.77129371 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + t = -3.77129371 + -0.6875 t = -3.77129371 + -0.6875 Combine like terms: -3.77129371 + -0.6875 = -4.45879371 t = -4.45879371 Simplifying t = -4.45879371Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.08379371, -4.45879371}Solution
t = {3.08379371, -4.45879371}
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