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Simplifying 5t2 + -40t = 70 Reorder the terms: -40t + 5t2 = 70 Solving -40t + 5t2 = 70 Solving for variable 't'. Reorder the terms: -70 + -40t + 5t2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + -40t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-14 + -8t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-14 + -8t + t2)' equal to zero and attempt to solve: Simplifying -14 + -8t + t2 = 0 Solving -14 + -8t + t2 = 0 Begin completing the square. 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 = 9.477225575 t = 9.477225575 Simplifying t = 9.477225575Subproblem 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 = -1.477225575 t = -1.477225575 Simplifying t = -1.477225575Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.477225575, -1.477225575}Solution
t = {9.477225575, -1.477225575}
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