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Simplifying 12x2 = 2x + 13 Reorder the terms: 12x2 = 13 + 2x Solving 12x2 = 13 + 2x Solving for variable 'x'. Reorder the terms: -13 + -2x + 12x2 = 13 + 2x + -13 + -2x Reorder the terms: -13 + -2x + 12x2 = 13 + -13 + 2x + -2x Combine like terms: 13 + -13 = 0 -13 + -2x + 12x2 = 0 + 2x + -2x -13 + -2x + 12x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -13 + -2x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.083333333 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + -0.1666666667x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + -0.1666666667x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 1.083333333 -0.1666666667x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 -0.1666666667x + x2 = 1.083333333 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 = 1.083333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 1.083333333 + 0.006944444447 Combine like terms: 1.083333333 + 0.006944444447 = 1.090277777447 0.006944444447 + -0.1666666667x + x2 = 1.090277777447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 1.090277777447 Calculate the square root of the right side: 1.044163674 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.044163674 and -1.044163674.Subproblem 1
x + -0.08333333335 = 1.044163674 Simplifying x + -0.08333333335 = 1.044163674 Reorder the terms: -0.08333333335 + x = 1.044163674 Solving -0.08333333335 + x = 1.044163674 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 = 1.044163674 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.044163674 + 0.08333333335 x = 1.044163674 + 0.08333333335 Combine like terms: 1.044163674 + 0.08333333335 = 1.12749700735 x = 1.12749700735 Simplifying x = 1.12749700735Subproblem 2
x + -0.08333333335 = -1.044163674 Simplifying x + -0.08333333335 = -1.044163674 Reorder the terms: -0.08333333335 + x = -1.044163674 Solving -0.08333333335 + x = -1.044163674 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 = -1.044163674 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.044163674 + 0.08333333335 x = -1.044163674 + 0.08333333335 Combine like terms: -1.044163674 + 0.08333333335 = -0.96083034065 x = -0.96083034065 Simplifying x = -0.96083034065Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.12749700735, -0.96083034065}
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