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Simplifying -12x2 + 11x + -6x2 + 4 = 0 Reorder the terms: 4 + 11x + -12x2 + -6x2 = 0 Combine like terms: -12x2 + -6x2 = -18x2 4 + 11x + -18x2 = 0 Solving 4 + 11x + -18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.2222222222 + -0.6111111111x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.6111111111x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.6111111111x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.6111111111x + x2 = 0 + 0.2222222222 -0.6111111111x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.6111111111x + x2 = 0.2222222222 The x term is -0.6111111111x. Take half its coefficient (-0.3055555556). Square it (0.09336419756) and add it to both sides. Add '0.09336419756' to each side of the equation. -0.6111111111x + 0.09336419756 + x2 = 0.2222222222 + 0.09336419756 Reorder the terms: 0.09336419756 + -0.6111111111x + x2 = 0.2222222222 + 0.09336419756 Combine like terms: 0.2222222222 + 0.09336419756 = 0.31558641976 0.09336419756 + -0.6111111111x + x2 = 0.31558641976 Factor a perfect square on the left side: (x + -0.3055555556)(x + -0.3055555556) = 0.31558641976 Calculate the square root of the right side: 0.561770789 Break this problem into two subproblems by setting (x + -0.3055555556) equal to 0.561770789 and -0.561770789.Subproblem 1
x + -0.3055555556 = 0.561770789 Simplifying x + -0.3055555556 = 0.561770789 Reorder the terms: -0.3055555556 + x = 0.561770789 Solving -0.3055555556 + x = 0.561770789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3055555556' to each side of the equation. -0.3055555556 + 0.3055555556 + x = 0.561770789 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = 0.561770789 + 0.3055555556 x = 0.561770789 + 0.3055555556 Combine like terms: 0.561770789 + 0.3055555556 = 0.8673263446 x = 0.8673263446 Simplifying x = 0.8673263446Subproblem 2
x + -0.3055555556 = -0.561770789 Simplifying x + -0.3055555556 = -0.561770789 Reorder the terms: -0.3055555556 + x = -0.561770789 Solving -0.3055555556 + x = -0.561770789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3055555556' to each side of the equation. -0.3055555556 + 0.3055555556 + x = -0.561770789 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = -0.561770789 + 0.3055555556 x = -0.561770789 + 0.3055555556 Combine like terms: -0.561770789 + 0.3055555556 = -0.2562152334 x = -0.2562152334 Simplifying x = -0.2562152334Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8673263446, -0.2562152334}
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