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Simplifying 24x2 + 4x + -2 = 0 Reorder the terms: -2 + 4x + 24x2 = 0 Solving -2 + 4x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2x + 12x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + 12x2 = 0 Solving -1 + 2x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.1666666667x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.1666666667x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.1666666667x + x2 = 0 + 0.08333333333 0.1666666667x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.1666666667x + x2 = 0.08333333333 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 0.08333333333 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 0.08333333333 + 0.006944444447 Combine like terms: 0.08333333333 + 0.006944444447 = 0.090277777777 0.006944444447 + 0.1666666667x + x2 = 0.090277777777 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 0.090277777777 Calculate the square root of the right side: 0.300462606 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 0.300462606 and -0.300462606.Subproblem 1
x + 0.08333333335 = 0.300462606 Simplifying x + 0.08333333335 = 0.300462606 Reorder the terms: 0.08333333335 + x = 0.300462606 Solving 0.08333333335 + x = 0.300462606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 0.300462606 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 0.300462606 + -0.08333333335 x = 0.300462606 + -0.08333333335 Combine like terms: 0.300462606 + -0.08333333335 = 0.21712927265 x = 0.21712927265 Simplifying x = 0.21712927265Subproblem 2
x + 0.08333333335 = -0.300462606 Simplifying x + 0.08333333335 = -0.300462606 Reorder the terms: 0.08333333335 + x = -0.300462606 Solving 0.08333333335 + x = -0.300462606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -0.300462606 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -0.300462606 + -0.08333333335 x = -0.300462606 + -0.08333333335 Combine like terms: -0.300462606 + -0.08333333335 = -0.38379593935 x = -0.38379593935 Simplifying x = -0.38379593935Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.21712927265, -0.38379593935}Solution
x = {0.21712927265, -0.38379593935}
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