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Simplifying 6x2 + 70x + 24 = 0 Reorder the terms: 24 + 70x + 6x2 = 0 Solving 24 + 70x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 35x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 35x + 3x2)' equal to zero and attempt to solve: Simplifying 12 + 35x + 3x2 = 0 Solving 12 + 35x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 11.66666667x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 11.66666667x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 11.66666667x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 11.66666667x + x2 = 0 + -4 11.66666667x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 11.66666667x + x2 = -4 The x term is 11.66666667x. Take half its coefficient (5.833333335). Square it (34.02777780) and add it to both sides. Add '34.02777780' to each side of the equation. 11.66666667x + 34.02777780 + x2 = -4 + 34.02777780 Reorder the terms: 34.02777780 + 11.66666667x + x2 = -4 + 34.02777780 Combine like terms: -4 + 34.02777780 = 30.0277778 34.02777780 + 11.66666667x + x2 = 30.0277778 Factor a perfect square on the left side: (x + 5.833333335)(x + 5.833333335) = 30.0277778 Calculate the square root of the right side: 5.479760743 Break this problem into two subproblems by setting (x + 5.833333335) equal to 5.479760743 and -5.479760743.Subproblem 1
x + 5.833333335 = 5.479760743 Simplifying x + 5.833333335 = 5.479760743 Reorder the terms: 5.833333335 + x = 5.479760743 Solving 5.833333335 + x = 5.479760743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.833333335' to each side of the equation. 5.833333335 + -5.833333335 + x = 5.479760743 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = 5.479760743 + -5.833333335 x = 5.479760743 + -5.833333335 Combine like terms: 5.479760743 + -5.833333335 = -0.353572592 x = -0.353572592 Simplifying x = -0.353572592Subproblem 2
x + 5.833333335 = -5.479760743 Simplifying x + 5.833333335 = -5.479760743 Reorder the terms: 5.833333335 + x = -5.479760743 Solving 5.833333335 + x = -5.479760743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.833333335' to each side of the equation. 5.833333335 + -5.833333335 + x = -5.479760743 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = -5.479760743 + -5.833333335 x = -5.479760743 + -5.833333335 Combine like terms: -5.479760743 + -5.833333335 = -11.313094078 x = -11.313094078 Simplifying x = -11.313094078Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.353572592, -11.313094078}Solution
x = {-0.353572592, -11.313094078}
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