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Simplifying 21 = 5t2 + 25t Reorder the terms: 21 = 25t + 5t2 Solving 21 = 25t + 5t2 Solving for variable 't'. Reorder the terms: 21 + -25t + -5t2 = 25t + -25t + 5t2 + -5t2 Combine like terms: 25t + -25t = 0 21 + -25t + -5t2 = 0 + 5t2 + -5t2 21 + -25t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 21 + -25t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.2 + 5t + t2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 5t + 4.2 + t2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 5t + t2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 5t + t2 = 0 + 4.2 5t + t2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 5t + t2 = 4.2 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 4.2 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 4.2 + 6.25 Combine like terms: 4.2 + 6.25 = 10.45 6.25 + 5t + t2 = 10.45 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 10.45 Calculate the square root of the right side: 3.232645975 Break this problem into two subproblems by setting (t + 2.5) equal to 3.232645975 and -3.232645975.Subproblem 1
t + 2.5 = 3.232645975 Simplifying t + 2.5 = 3.232645975 Reorder the terms: 2.5 + t = 3.232645975 Solving 2.5 + t = 3.232645975 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 3.232645975 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 3.232645975 + -2.5 t = 3.232645975 + -2.5 Combine like terms: 3.232645975 + -2.5 = 0.732645975 t = 0.732645975 Simplifying t = 0.732645975Subproblem 2
t + 2.5 = -3.232645975 Simplifying t + 2.5 = -3.232645975 Reorder the terms: 2.5 + t = -3.232645975 Solving 2.5 + t = -3.232645975 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -3.232645975 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -3.232645975 + -2.5 t = -3.232645975 + -2.5 Combine like terms: -3.232645975 + -2.5 = -5.732645975 t = -5.732645975 Simplifying t = -5.732645975Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.732645975, -5.732645975}
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