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Simplifying 21t2 + -18t + 3 = 0 Reorder the terms: 3 + -18t + 21t2 = 0 Solving 3 + -18t + 21t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -6t + 7t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -6t + 7t2)' equal to zero and attempt to solve: Simplifying 1 + -6t + 7t2 = 0 Solving 1 + -6t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -0.8571428571t + t2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.8571428571t + -0.1428571429 + t2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -0.8571428571t + t2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -0.8571428571t + t2 = 0 + -0.1428571429 -0.8571428571t + t2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -0.8571428571t + t2 = -0.1428571429 The t term is -0.8571428571t. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571t + 0.1836734694 + t2 = -0.1428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571t + t2 = -0.1428571429 + 0.1836734694 Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265 0.1836734694 + -0.8571428571t + t2 = 0.0408163265 Factor a perfect square on the left side: (t + -0.4285714286)(t + -0.4285714286) = 0.0408163265 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (t + -0.4285714286) equal to 0.202030509 and -0.202030509.Subproblem 1
t + -0.4285714286 = 0.202030509 Simplifying t + -0.4285714286 = 0.202030509 Reorder the terms: -0.4285714286 + t = 0.202030509 Solving -0.4285714286 + t = 0.202030509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + t = 0.202030509 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + t = 0.202030509 + 0.4285714286 t = 0.202030509 + 0.4285714286 Combine like terms: 0.202030509 + 0.4285714286 = 0.6306019376 t = 0.6306019376 Simplifying t = 0.6306019376Subproblem 2
t + -0.4285714286 = -0.202030509 Simplifying t + -0.4285714286 = -0.202030509 Reorder the terms: -0.4285714286 + t = -0.202030509 Solving -0.4285714286 + t = -0.202030509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + t = -0.202030509 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + t = -0.202030509 + 0.4285714286 t = -0.202030509 + 0.4285714286 Combine like terms: -0.202030509 + 0.4285714286 = 0.2265409196 t = 0.2265409196 Simplifying t = 0.2265409196Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6306019376, 0.2265409196}Solution
t = {0.6306019376, 0.2265409196}
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