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Simplifying 4t2 + -21t + 8 = 0 Reorder the terms: 8 + -21t + 4t2 = 0 Solving 8 + -21t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + -5.25t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5.25t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -5.25t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5.25t + t2 = 0 + -2 -5.25t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5.25t + t2 = -2 The t term is -5.25t. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25t + 6.890625 + t2 = -2 + 6.890625 Reorder the terms: 6.890625 + -5.25t + t2 = -2 + 6.890625 Combine like terms: -2 + 6.890625 = 4.890625 6.890625 + -5.25t + t2 = 4.890625 Factor a perfect square on the left side: (t + -2.625)(t + -2.625) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (t + -2.625) equal to 2.211475752 and -2.211475752.Subproblem 1
t + -2.625 = 2.211475752 Simplifying t + -2.625 = 2.211475752 Reorder the terms: -2.625 + t = 2.211475752 Solving -2.625 + t = 2.211475752 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + t = 2.211475752 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + t = 2.211475752 + 2.625 t = 2.211475752 + 2.625 Combine like terms: 2.211475752 + 2.625 = 4.836475752 t = 4.836475752 Simplifying t = 4.836475752Subproblem 2
t + -2.625 = -2.211475752 Simplifying t + -2.625 = -2.211475752 Reorder the terms: -2.625 + t = -2.211475752 Solving -2.625 + t = -2.211475752 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + t = -2.211475752 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + t = -2.211475752 + 2.625 t = -2.211475752 + 2.625 Combine like terms: -2.211475752 + 2.625 = 0.413524248 t = 0.413524248 Simplifying t = 0.413524248Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.836475752, 0.413524248}
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