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Simplifying 25 = 0.3t2 + 5t Reorder the terms: 25 = 5t + 0.3t2 Solving 25 = 5t + 0.3t2 Solving for variable 't'. Reorder the terms: 25 + -5t + -0.3t2 = 5t + -5t + 0.3t2 + -0.3t2 Combine like terms: 5t + -5t = 0 25 + -5t + -0.3t2 = 0 + 0.3t2 + -0.3t2 25 + -5t + -0.3t2 = 0.3t2 + -0.3t2 Combine like terms: 0.3t2 + -0.3t2 = 0.0 25 + -5t + -0.3t2 = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -83.33333333 + 16.66666667t + t2 = 0 Move the constant term to the right: Add '83.33333333' to each side of the equation. -83.33333333 + 16.66666667t + 83.33333333 + t2 = 0 + 83.33333333 Reorder the terms: -83.33333333 + 83.33333333 + 16.66666667t + t2 = 0 + 83.33333333 Combine like terms: -83.33333333 + 83.33333333 = 0.00000000 0.00000000 + 16.66666667t + t2 = 0 + 83.33333333 16.66666667t + t2 = 0 + 83.33333333 Combine like terms: 0 + 83.33333333 = 83.33333333 16.66666667t + t2 = 83.33333333 The t term is 16.66666667t. Take half its coefficient (8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. 16.66666667t + 69.44444447 + t2 = 83.33333333 + 69.44444447 Reorder the terms: 69.44444447 + 16.66666667t + t2 = 83.33333333 + 69.44444447 Combine like terms: 83.33333333 + 69.44444447 = 152.7777778 69.44444447 + 16.66666667t + t2 = 152.7777778 Factor a perfect square on the left side: (t + 8.333333335)(t + 8.333333335) = 152.7777778 Calculate the square root of the right side: 12.360330813 Break this problem into two subproblems by setting (t + 8.333333335) equal to 12.360330813 and -12.360330813.Subproblem 1
t + 8.333333335 = 12.360330813 Simplifying t + 8.333333335 = 12.360330813 Reorder the terms: 8.333333335 + t = 12.360330813 Solving 8.333333335 + t = 12.360330813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.333333335' to each side of the equation. 8.333333335 + -8.333333335 + t = 12.360330813 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + t = 12.360330813 + -8.333333335 t = 12.360330813 + -8.333333335 Combine like terms: 12.360330813 + -8.333333335 = 4.026997478 t = 4.026997478 Simplifying t = 4.026997478Subproblem 2
t + 8.333333335 = -12.360330813 Simplifying t + 8.333333335 = -12.360330813 Reorder the terms: 8.333333335 + t = -12.360330813 Solving 8.333333335 + t = -12.360330813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.333333335' to each side of the equation. 8.333333335 + -8.333333335 + t = -12.360330813 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + t = -12.360330813 + -8.333333335 t = -12.360330813 + -8.333333335 Combine like terms: -12.360330813 + -8.333333335 = -20.693664148 t = -20.693664148 Simplifying t = -20.693664148Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.026997478, -20.693664148}
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