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Simplifying 4t2 + 21t + 18 = 0 Reorder the terms: 18 + 21t + 4t2 = 0 Solving 18 + 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'. 4.5 + 5.25t + t2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 5.25t + -4.5 + t2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 5.25t + t2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 5.25t + t2 = 0 + -4.5 5.25t + t2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 5.25t + t2 = -4.5 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 = -4.5 + 6.890625 Reorder the terms: 6.890625 + 5.25t + t2 = -4.5 + 6.890625 Combine like terms: -4.5 + 6.890625 = 2.390625 6.890625 + 5.25t + t2 = 2.390625 Factor a perfect square on the left side: (t + 2.625)(t + 2.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (t + 2.625) equal to 1.54616461 and -1.54616461.Subproblem 1
t + 2.625 = 1.54616461 Simplifying t + 2.625 = 1.54616461 Reorder the terms: 2.625 + t = 1.54616461 Solving 2.625 + t = 1.54616461 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 = 1.54616461 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + t = 1.54616461 + -2.625 t = 1.54616461 + -2.625 Combine like terms: 1.54616461 + -2.625 = -1.07883539 t = -1.07883539 Simplifying t = -1.07883539Subproblem 2
t + 2.625 = -1.54616461 Simplifying t + 2.625 = -1.54616461 Reorder the terms: 2.625 + t = -1.54616461 Solving 2.625 + t = -1.54616461 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 = -1.54616461 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + t = -1.54616461 + -2.625 t = -1.54616461 + -2.625 Combine like terms: -1.54616461 + -2.625 = -4.17116461 t = -4.17116461 Simplifying t = -4.17116461Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.07883539, -4.17116461}
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