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Simplifying 30 = 14t + 5t2 Solving 30 = 14t + 5t2 Solving for variable 't'. Reorder the terms: 30 + -14t + -5t2 = 14t + -14t + 5t2 + -5t2 Combine like terms: 14t + -14t = 0 30 + -14t + -5t2 = 0 + 5t2 + -5t2 30 + -14t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 30 + -14t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6 + 2.8t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 2.8t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + 2.8t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2.8t + t2 = 0 + 6 2.8t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 2.8t + t2 = 6 The t term is 2.8t. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8t + 1.96 + t2 = 6 + 1.96 Reorder the terms: 1.96 + 2.8t + t2 = 6 + 1.96 Combine like terms: 6 + 1.96 = 7.96 1.96 + 2.8t + t2 = 7.96 Factor a perfect square on the left side: (t + 1.4)(t + 1.4) = 7.96 Calculate the square root of the right side: 2.821347196 Break this problem into two subproblems by setting (t + 1.4) equal to 2.821347196 and -2.821347196.Subproblem 1
t + 1.4 = 2.821347196 Simplifying t + 1.4 = 2.821347196 Reorder the terms: 1.4 + t = 2.821347196 Solving 1.4 + t = 2.821347196 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + t = 2.821347196 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + t = 2.821347196 + -1.4 t = 2.821347196 + -1.4 Combine like terms: 2.821347196 + -1.4 = 1.421347196 t = 1.421347196 Simplifying t = 1.421347196Subproblem 2
t + 1.4 = -2.821347196 Simplifying t + 1.4 = -2.821347196 Reorder the terms: 1.4 + t = -2.821347196 Solving 1.4 + t = -2.821347196 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + t = -2.821347196 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + t = -2.821347196 + -1.4 t = -2.821347196 + -1.4 Combine like terms: -2.821347196 + -1.4 = -4.221347196 t = -4.221347196 Simplifying t = -4.221347196Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.421347196, -4.221347196}
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