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Simplifying 12x2 + 2x + -3 = 50 Reorder the terms: -3 + 2x + 12x2 = 50 Solving -3 + 2x + 12x2 = 50 Solving for variable 'x'. Reorder the terms: -3 + -50 + 2x + 12x2 = 50 + -50 Combine like terms: -3 + -50 = -53 -53 + 2x + 12x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -53 + 2x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4.416666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '4.416666667' to each side of the equation. -4.416666667 + 0.1666666667x + 4.416666667 + x2 = 0 + 4.416666667 Reorder the terms: -4.416666667 + 4.416666667 + 0.1666666667x + x2 = 0 + 4.416666667 Combine like terms: -4.416666667 + 4.416666667 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 4.416666667 0.1666666667x + x2 = 0 + 4.416666667 Combine like terms: 0 + 4.416666667 = 4.416666667 0.1666666667x + x2 = 4.416666667 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 = 4.416666667 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 4.416666667 + 0.006944444447 Combine like terms: 4.416666667 + 0.006944444447 = 4.423611111447 0.006944444447 + 0.1666666667x + x2 = 4.423611111447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 4.423611111447 Calculate the square root of the right side: 2.103238244 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 2.103238244 and -2.103238244.Subproblem 1
x + 0.08333333335 = 2.103238244 Simplifying x + 0.08333333335 = 2.103238244 Reorder the terms: 0.08333333335 + x = 2.103238244 Solving 0.08333333335 + x = 2.103238244 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 = 2.103238244 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 2.103238244 + -0.08333333335 x = 2.103238244 + -0.08333333335 Combine like terms: 2.103238244 + -0.08333333335 = 2.01990491065 x = 2.01990491065 Simplifying x = 2.01990491065Subproblem 2
x + 0.08333333335 = -2.103238244 Simplifying x + 0.08333333335 = -2.103238244 Reorder the terms: 0.08333333335 + x = -2.103238244 Solving 0.08333333335 + x = -2.103238244 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 = -2.103238244 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -2.103238244 + -0.08333333335 x = -2.103238244 + -0.08333333335 Combine like terms: -2.103238244 + -0.08333333335 = -2.18657157735 x = -2.18657157735 Simplifying x = -2.18657157735Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.01990491065, -2.18657157735}
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