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Simplifying 12x2 + -2x + -3 = 0 Reorder the terms: -3 + -2x + 12x2 = 0 Solving -3 + -2x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.25 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.1666666667x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.1666666667x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.1666666667x + x2 = 0 + 0.25 -0.1666666667x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.1666666667x + x2 = 0.25 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 = 0.25 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 0.25 + 0.006944444447 Combine like terms: 0.25 + 0.006944444447 = 0.256944444447 0.006944444447 + -0.1666666667x + x2 = 0.256944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 0.256944444447 Calculate the square root of the right side: 0.506896878 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 0.506896878 and -0.506896878.Subproblem 1
x + -0.08333333335 = 0.506896878 Simplifying x + -0.08333333335 = 0.506896878 Reorder the terms: -0.08333333335 + x = 0.506896878 Solving -0.08333333335 + x = 0.506896878 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 = 0.506896878 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.506896878 + 0.08333333335 x = 0.506896878 + 0.08333333335 Combine like terms: 0.506896878 + 0.08333333335 = 0.59023021135 x = 0.59023021135 Simplifying x = 0.59023021135Subproblem 2
x + -0.08333333335 = -0.506896878 Simplifying x + -0.08333333335 = -0.506896878 Reorder the terms: -0.08333333335 + x = -0.506896878 Solving -0.08333333335 + x = -0.506896878 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 = -0.506896878 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.506896878 + 0.08333333335 x = -0.506896878 + 0.08333333335 Combine like terms: -0.506896878 + 0.08333333335 = -0.42356354465 x = -0.42356354465 Simplifying x = -0.42356354465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.59023021135, -0.42356354465}
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