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Simplifying (-1t2) + 8t + 21 = 0 Reorder the terms: 21 + 8t + (-1t2) = 0 Solving 21 + 8t + (-1t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -8t + t2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -8t + 21 + t2 = 0 + 21 Reorder the terms: -21 + 21 + -8t + t2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -8t + t2 = 0 + 21 -8t + t2 = 0 + 21 Combine like terms: 0 + 21 = 21 -8t + t2 = 21 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 21 + 16 Reorder the terms: 16 + -8t + t2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + -8t + t2 = 37 Factor a perfect square on the left side: ((t) + -4)((t) + -4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting ((t) + -4) equal to 6.08276253 and -6.08276253.Subproblem 1
(t) + -4 = 6.08276253 Simplifying (t) + -4 = 6.08276253 t + -4 = 6.08276253 Reorder the terms: -4 + t = 6.08276253 Solving -4 + t = 6.08276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + t = 6.08276253 + 4 t = 6.08276253 + 4 Combine like terms: 6.08276253 + 4 = 10.08276253 t = 10.08276253 Simplifying t = 10.08276253Subproblem 2
(t) + -4 = -6.08276253 Simplifying (t) + -4 = -6.08276253 t + -4 = -6.08276253 Reorder the terms: -4 + t = -6.08276253 Solving -4 + t = -6.08276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + t = -6.08276253 + 4 t = -6.08276253 + 4 Combine like terms: -6.08276253 + 4 = -2.08276253 t = -2.08276253 Simplifying t = -2.08276253Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.08276253, -2.08276253}
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