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Simplifying 1t2 + 21t = 8 Reorder the terms: 21t + 1t2 = 8 Solving 21t + 1t2 = 8 Solving for variable 't'. Reorder the terms: -8 + 21t + 1t2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 21t + 1t2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 21t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 21t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 21t + t2 = 0 + 8 21t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 21t + t2 = 8 The t term is 21t. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21t + 110.25 + t2 = 8 + 110.25 Reorder the terms: 110.25 + 21t + t2 = 8 + 110.25 Combine like terms: 8 + 110.25 = 118.25 110.25 + 21t + t2 = 118.25 Factor a perfect square on the left side: (t + 10.5)(t + 10.5) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (t + 10.5) equal to 10.874281585 and -10.874281585.Subproblem 1
t + 10.5 = 10.874281585 Simplifying t + 10.5 = 10.874281585 Reorder the terms: 10.5 + t = 10.874281585 Solving 10.5 + t = 10.874281585 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + t = 10.874281585 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + t = 10.874281585 + -10.5 t = 10.874281585 + -10.5 Combine like terms: 10.874281585 + -10.5 = 0.374281585 t = 0.374281585 Simplifying t = 0.374281585Subproblem 2
t + 10.5 = -10.874281585 Simplifying t + 10.5 = -10.874281585 Reorder the terms: 10.5 + t = -10.874281585 Solving 10.5 + t = -10.874281585 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + t = -10.874281585 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + t = -10.874281585 + -10.5 t = -10.874281585 + -10.5 Combine like terms: -10.874281585 + -10.5 = -21.374281585 t = -21.374281585 Simplifying t = -21.374281585Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.374281585, -21.374281585}
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