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Simplifying 70 = 40t + 5t2 Solving 70 = 40t + 5t2 Solving for variable 't'. Reorder the terms: 70 + -40t + -5t2 = 40t + -40t + 5t2 + -5t2 Combine like terms: 40t + -40t = 0 70 + -40t + -5t2 = 0 + 5t2 + -5t2 70 + -40t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 70 + -40t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(14 + -8t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(14 + -8t + -1t2)' equal to zero and attempt to solve: Simplifying 14 + -8t + -1t2 = 0 Solving 14 + -8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 8t + t2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 8t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + 8t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 8t + t2 = 0 + 14 8t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 8t + t2 = 14 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = 14 + 16 Reorder the terms: 16 + 8t + t2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + 8t + t2 = 30 Factor a perfect square on the left side: (t + 4)(t + 4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (t + 4) equal to 5.477225575 and -5.477225575.Subproblem 1
t + 4 = 5.477225575 Simplifying t + 4 = 5.477225575 Reorder the terms: 4 + t = 5.477225575 Solving 4 + t = 5.477225575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + t = 5.477225575 + -4 t = 5.477225575 + -4 Combine like terms: 5.477225575 + -4 = 1.477225575 t = 1.477225575 Simplifying t = 1.477225575Subproblem 2
t + 4 = -5.477225575 Simplifying t + 4 = -5.477225575 Reorder the terms: 4 + t = -5.477225575 Solving 4 + t = -5.477225575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + t = -5.477225575 + -4 t = -5.477225575 + -4 Combine like terms: -5.477225575 + -4 = -9.477225575 t = -9.477225575 Simplifying t = -9.477225575Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.477225575, -9.477225575}Solution
t = {1.477225575, -9.477225575}
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