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Simplifying (t) = -5t2 + 30t + 80 t = -5t2 + 30t + 80 Reorder the terms: t = 80 + 30t + -5t2 Solving t = 80 + 30t + -5t2 Solving for variable 't'. Reorder the terms: -80 + t + -30t + 5t2 = 80 + 30t + -5t2 + -80 + -30t + 5t2 Combine like terms: t + -30t = -29t -80 + -29t + 5t2 = 80 + 30t + -5t2 + -80 + -30t + 5t2 Reorder the terms: -80 + -29t + 5t2 = 80 + -80 + 30t + -30t + -5t2 + 5t2 Combine like terms: 80 + -80 = 0 -80 + -29t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2 -80 + -29t + 5t2 = 30t + -30t + -5t2 + 5t2 Combine like terms: 30t + -30t = 0 -80 + -29t + 5t2 = 0 + -5t2 + 5t2 -80 + -29t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -80 + -29t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + -5.8t + t2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -5.8t + 16 + t2 = 0 + 16 Reorder the terms: -16 + 16 + -5.8t + t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5.8t + t2 = 0 + 16 -5.8t + t2 = 0 + 16 Combine like terms: 0 + 16 = 16 -5.8t + t2 = 16 The t term is -5.8t. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8t + 8.41 + t2 = 16 + 8.41 Reorder the terms: 8.41 + -5.8t + t2 = 16 + 8.41 Combine like terms: 16 + 8.41 = 24.41 8.41 + -5.8t + t2 = 24.41 Factor a perfect square on the left side: (t + -2.9)(t + -2.9) = 24.41 Calculate the square root of the right side: 4.940647731 Break this problem into two subproblems by setting (t + -2.9) equal to 4.940647731 and -4.940647731.Subproblem 1
t + -2.9 = 4.940647731 Simplifying t + -2.9 = 4.940647731 Reorder the terms: -2.9 + t = 4.940647731 Solving -2.9 + t = 4.940647731 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + t = 4.940647731 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + t = 4.940647731 + 2.9 t = 4.940647731 + 2.9 Combine like terms: 4.940647731 + 2.9 = 7.840647731 t = 7.840647731 Simplifying t = 7.840647731Subproblem 2
t + -2.9 = -4.940647731 Simplifying t + -2.9 = -4.940647731 Reorder the terms: -2.9 + t = -4.940647731 Solving -2.9 + t = -4.940647731 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + t = -4.940647731 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + t = -4.940647731 + 2.9 t = -4.940647731 + 2.9 Combine like terms: -4.940647731 + 2.9 = -2.040647731 t = -2.040647731 Simplifying t = -2.040647731Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.840647731, -2.040647731}
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