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Simplifying 6x2 + -1x + -32 = 0 Reorder the terms: -32 + -1x + 6x2 = 0 Solving -32 + -1x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.333333333 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -0.1666666667x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -0.1666666667x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 5.333333333 -0.1666666667x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -0.1666666667x + x2 = 5.333333333 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 = 5.333333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 5.333333333 + 0.006944444447 Combine like terms: 5.333333333 + 0.006944444447 = 5.340277777447 0.006944444447 + -0.1666666667x + x2 = 5.340277777447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 5.340277777447 Calculate the square root of the right side: 2.310904104 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 2.310904104 and -2.310904104.Subproblem 1
x + -0.08333333335 = 2.310904104 Simplifying x + -0.08333333335 = 2.310904104 Reorder the terms: -0.08333333335 + x = 2.310904104 Solving -0.08333333335 + x = 2.310904104 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 = 2.310904104 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 2.310904104 + 0.08333333335 x = 2.310904104 + 0.08333333335 Combine like terms: 2.310904104 + 0.08333333335 = 2.39423743735 x = 2.39423743735 Simplifying x = 2.39423743735Subproblem 2
x + -0.08333333335 = -2.310904104 Simplifying x + -0.08333333335 = -2.310904104 Reorder the terms: -0.08333333335 + x = -2.310904104 Solving -0.08333333335 + x = -2.310904104 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 = -2.310904104 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -2.310904104 + 0.08333333335 x = -2.310904104 + 0.08333333335 Combine like terms: -2.310904104 + 0.08333333335 = -2.22757077065 x = -2.22757077065 Simplifying x = -2.22757077065Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.39423743735, -2.22757077065}
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