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Simplifying 150 = 14t2 + -120t Reorder the terms: 150 = -120t + 14t2 Solving 150 = -120t + 14t2 Solving for variable 't'. Reorder the terms: 150 + 120t + -14t2 = -120t + 120t + 14t2 + -14t2 Combine like terms: -120t + 120t = 0 150 + 120t + -14t2 = 0 + 14t2 + -14t2 150 + 120t + -14t2 = 14t2 + -14t2 Combine like terms: 14t2 + -14t2 = 0 150 + 120t + -14t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + 60t + -7t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + 60t + -7t2)' equal to zero and attempt to solve: Simplifying 75 + 60t + -7t2 = 0 Solving 75 + 60t + -7t2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -10.71428571 + -8.571428571t + t2 = 0 Move the constant term to the right: Add '10.71428571' to each side of the equation. -10.71428571 + -8.571428571t + 10.71428571 + t2 = 0 + 10.71428571 Reorder the terms: -10.71428571 + 10.71428571 + -8.571428571t + t2 = 0 + 10.71428571 Combine like terms: -10.71428571 + 10.71428571 = 0.00000000 0.00000000 + -8.571428571t + t2 = 0 + 10.71428571 -8.571428571t + t2 = 0 + 10.71428571 Combine like terms: 0 + 10.71428571 = 10.71428571 -8.571428571t + t2 = 10.71428571 The t term is -8.571428571t. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571t + 18.36734694 + t2 = 10.71428571 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571t + t2 = 10.71428571 + 18.36734694 Combine like terms: 10.71428571 + 18.36734694 = 29.08163265 18.36734694 + -8.571428571t + t2 = 29.08163265 Factor a perfect square on the left side: (t + -4.285714286)(t + -4.285714286) = 29.08163265 Calculate the square root of the right side: 5.392738882 Break this problem into two subproblems by setting (t + -4.285714286) equal to 5.392738882 and -5.392738882.Subproblem 1
t + -4.285714286 = 5.392738882 Simplifying t + -4.285714286 = 5.392738882 Reorder the terms: -4.285714286 + t = 5.392738882 Solving -4.285714286 + t = 5.392738882 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + t = 5.392738882 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + t = 5.392738882 + 4.285714286 t = 5.392738882 + 4.285714286 Combine like terms: 5.392738882 + 4.285714286 = 9.678453168 t = 9.678453168 Simplifying t = 9.678453168Subproblem 2
t + -4.285714286 = -5.392738882 Simplifying t + -4.285714286 = -5.392738882 Reorder the terms: -4.285714286 + t = -5.392738882 Solving -4.285714286 + t = -5.392738882 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + t = -5.392738882 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + t = -5.392738882 + 4.285714286 t = -5.392738882 + 4.285714286 Combine like terms: -5.392738882 + 4.285714286 = -1.107024596 t = -1.107024596 Simplifying t = -1.107024596Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.678453168, -1.107024596}Solution
t = {9.678453168, -1.107024596}
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