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Simplifying 24x2 + -14x + -6 = 0 Reorder the terms: -6 + -14x + 24x2 = 0 Solving -6 + -14x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -7x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -7x + 12x2)' equal to zero and attempt to solve: Simplifying -3 + -7x + 12x2 = 0 Solving -3 + -7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.25 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.5833333333x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.5833333333x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.5833333333x + x2 = 0 + 0.25 -0.5833333333x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.5833333333x + x2 = 0.25 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 0.25 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 0.25 + 0.08506944446 Combine like terms: 0.25 + 0.08506944446 = 0.33506944446 0.08506944446 + -0.5833333333x + x2 = 0.33506944446 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.33506944446 Calculate the square root of the right side: 0.578851833 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.578851833 and -0.578851833.Subproblem 1
x + -0.2916666667 = 0.578851833 Simplifying x + -0.2916666667 = 0.578851833 Reorder the terms: -0.2916666667 + x = 0.578851833 Solving -0.2916666667 + x = 0.578851833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.578851833 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.578851833 + 0.2916666667 x = 0.578851833 + 0.2916666667 Combine like terms: 0.578851833 + 0.2916666667 = 0.8705184997 x = 0.8705184997 Simplifying x = 0.8705184997Subproblem 2
x + -0.2916666667 = -0.578851833 Simplifying x + -0.2916666667 = -0.578851833 Reorder the terms: -0.2916666667 + x = -0.578851833 Solving -0.2916666667 + x = -0.578851833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.578851833 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.578851833 + 0.2916666667 x = -0.578851833 + 0.2916666667 Combine like terms: -0.578851833 + 0.2916666667 = -0.2871851663 x = -0.2871851663 Simplifying x = -0.2871851663Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8705184997, -0.2871851663}Solution
x = {0.8705184997, -0.2871851663}
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