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Simplifying 18t2 + -14t + -14 = 0 Reorder the terms: -14 + -14t + 18t2 = 0 Solving -14 + -14t + 18t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -7t + 9t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -7t + 9t2)' equal to zero and attempt to solve: Simplifying -7 + -7t + 9t2 = 0 Solving -7 + -7t + 9t2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -0.7777777778t + t2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -0.7777777778t + 0.7777777778 + t2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -0.7777777778t + t2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -0.7777777778t + t2 = 0 + 0.7777777778 -0.7777777778t + t2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -0.7777777778t + t2 = 0.7777777778 The t term is -0.7777777778t. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778t + 0.1512345679 + t2 = 0.7777777778 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778t + t2 = 0.7777777778 + 0.1512345679 Combine like terms: 0.7777777778 + 0.1512345679 = 0.9290123457 0.1512345679 + -0.7777777778t + t2 = 0.9290123457 Factor a perfect square on the left side: (t + -0.3888888889)(t + -0.3888888889) = 0.9290123457 Calculate the square root of the right side: 0.963852865 Break this problem into two subproblems by setting (t + -0.3888888889) equal to 0.963852865 and -0.963852865.Subproblem 1
t + -0.3888888889 = 0.963852865 Simplifying t + -0.3888888889 = 0.963852865 Reorder the terms: -0.3888888889 + t = 0.963852865 Solving -0.3888888889 + t = 0.963852865 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + t = 0.963852865 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + t = 0.963852865 + 0.3888888889 t = 0.963852865 + 0.3888888889 Combine like terms: 0.963852865 + 0.3888888889 = 1.3527417539 t = 1.3527417539 Simplifying t = 1.3527417539Subproblem 2
t + -0.3888888889 = -0.963852865 Simplifying t + -0.3888888889 = -0.963852865 Reorder the terms: -0.3888888889 + t = -0.963852865 Solving -0.3888888889 + t = -0.963852865 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + t = -0.963852865 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + t = -0.963852865 + 0.3888888889 t = -0.963852865 + 0.3888888889 Combine like terms: -0.963852865 + 0.3888888889 = -0.5749639761 t = -0.5749639761 Simplifying t = -0.5749639761Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3527417539, -0.5749639761}Solution
t = {1.3527417539, -0.5749639761}
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