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Simplifying 25t2 + t + -420 = 0 Reorder the terms: -420 + t + 25t2 = 0 Solving -420 + t + 25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -16.8 + 0.04t + t2 = 0 Move the constant term to the right: Add '16.8' to each side of the equation. -16.8 + 0.04t + 16.8 + t2 = 0 + 16.8 Reorder the terms: -16.8 + 16.8 + 0.04t + t2 = 0 + 16.8 Combine like terms: -16.8 + 16.8 = 0.0 0.0 + 0.04t + t2 = 0 + 16.8 0.04t + t2 = 0 + 16.8 Combine like terms: 0 + 16.8 = 16.8 0.04t + t2 = 16.8 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.04t + 0.25 + t2 = 16.8 + 0.25 Reorder the terms: 0.25 + 0.04t + t2 = 16.8 + 0.25 Combine like terms: 16.8 + 0.25 = 17.05 0.25 + 0.04t + t2 = 17.05 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 17.05 Calculate the square root of the right side: 4.129164564 Break this problem into two subproblems by setting (t + 0.5) equal to 4.129164564 and -4.129164564.Subproblem 1
t + 0.5 = 4.129164564 Simplifying t + 0.5 = 4.129164564 Reorder the terms: 0.5 + t = 4.129164564 Solving 0.5 + t = 4.129164564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 4.129164564 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 4.129164564 + -0.5 t = 4.129164564 + -0.5 Combine like terms: 4.129164564 + -0.5 = 3.629164564 t = 3.629164564 Simplifying t = 3.629164564Subproblem 2
t + 0.5 = -4.129164564 Simplifying t + 0.5 = -4.129164564 Reorder the terms: 0.5 + t = -4.129164564 Solving 0.5 + t = -4.129164564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -4.129164564 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -4.129164564 + -0.5 t = -4.129164564 + -0.5 Combine like terms: -4.129164564 + -0.5 = -4.629164564 t = -4.629164564 Simplifying t = -4.629164564Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.629164564, -4.629164564}
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