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Simplifying 12x2 + 3x = 17 + x Reorder the terms: 3x + 12x2 = 17 + x Solving 3x + 12x2 = 17 + x Solving for variable 'x'. Reorder the terms: -17 + 3x + -1x + 12x2 = 17 + x + -17 + -1x Combine like terms: 3x + -1x = 2x -17 + 2x + 12x2 = 17 + x + -17 + -1x Reorder the terms: -17 + 2x + 12x2 = 17 + -17 + x + -1x Combine like terms: 17 + -17 = 0 -17 + 2x + 12x2 = 0 + x + -1x -17 + 2x + 12x2 = x + -1x Combine like terms: x + -1x = 0 -17 + 2x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.416666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.416666667' to each side of the equation. -1.416666667 + 0.1666666667x + 1.416666667 + x2 = 0 + 1.416666667 Reorder the terms: -1.416666667 + 1.416666667 + 0.1666666667x + x2 = 0 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 1.416666667 0.1666666667x + x2 = 0 + 1.416666667 Combine like terms: 0 + 1.416666667 = 1.416666667 0.1666666667x + x2 = 1.416666667 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 = 1.416666667 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 1.416666667 + 0.006944444447 Combine like terms: 1.416666667 + 0.006944444447 = 1.423611111447 0.006944444447 + 0.1666666667x + x2 = 1.423611111447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 1.423611111447 Calculate the square root of the right side: 1.193151755 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 1.193151755 and -1.193151755.Subproblem 1
x + 0.08333333335 = 1.193151755 Simplifying x + 0.08333333335 = 1.193151755 Reorder the terms: 0.08333333335 + x = 1.193151755 Solving 0.08333333335 + x = 1.193151755 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 = 1.193151755 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.193151755 + -0.08333333335 x = 1.193151755 + -0.08333333335 Combine like terms: 1.193151755 + -0.08333333335 = 1.10981842165 x = 1.10981842165 Simplifying x = 1.10981842165Subproblem 2
x + 0.08333333335 = -1.193151755 Simplifying x + 0.08333333335 = -1.193151755 Reorder the terms: 0.08333333335 + x = -1.193151755 Solving 0.08333333335 + x = -1.193151755 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 = -1.193151755 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.193151755 + -0.08333333335 x = -1.193151755 + -0.08333333335 Combine like terms: -1.193151755 + -0.08333333335 = -1.27648508835 x = -1.27648508835 Simplifying x = -1.27648508835Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.10981842165, -1.27648508835}
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