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Simplifying -0.25t2 + 9t + 26 = 0 Reorder the terms: 26 + 9t + -0.25t2 = 0 Solving 26 + 9t + -0.25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -104 + -36t + t2 = 0 Move the constant term to the right: Add '104' to each side of the equation. -104 + -36t + 104 + t2 = 0 + 104 Reorder the terms: -104 + 104 + -36t + t2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -36t + t2 = 0 + 104 -36t + t2 = 0 + 104 Combine like terms: 0 + 104 = 104 -36t + t2 = 104 The t term is -36t. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36t + 324 + t2 = 104 + 324 Reorder the terms: 324 + -36t + t2 = 104 + 324 Combine like terms: 104 + 324 = 428 324 + -36t + t2 = 428 Factor a perfect square on the left side: (t + -18)(t + -18) = 428 Calculate the square root of the right side: 20.688160866 Break this problem into two subproblems by setting (t + -18) equal to 20.688160866 and -20.688160866.Subproblem 1
t + -18 = 20.688160866 Simplifying t + -18 = 20.688160866 Reorder the terms: -18 + t = 20.688160866 Solving -18 + t = 20.688160866 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = 20.688160866 + 18 Combine like terms: -18 + 18 = 0 0 + t = 20.688160866 + 18 t = 20.688160866 + 18 Combine like terms: 20.688160866 + 18 = 38.688160866 t = 38.688160866 Simplifying t = 38.688160866Subproblem 2
t + -18 = -20.688160866 Simplifying t + -18 = -20.688160866 Reorder the terms: -18 + t = -20.688160866 Solving -18 + t = -20.688160866 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = -20.688160866 + 18 Combine like terms: -18 + 18 = 0 0 + t = -20.688160866 + 18 t = -20.688160866 + 18 Combine like terms: -20.688160866 + 18 = -2.688160866 t = -2.688160866 Simplifying t = -2.688160866Solution
The solution to the problem is based on the solutions from the subproblems. t = {38.688160866, -2.688160866}
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