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Simplifying 22 = 3x2 + -18x Reorder the terms: 22 = -18x + 3x2 Solving 22 = -18x + 3x2 Solving for variable 'x'. Reorder the terms: 22 + 18x + -3x2 = -18x + 18x + 3x2 + -3x2 Combine like terms: -18x + 18x = 0 22 + 18x + -3x2 = 0 + 3x2 + -3x2 22 + 18x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 22 + 18x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + -6x + 7.333333333 + x2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + -6x + x2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + 7.333333333 -6x + x2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 -6x + x2 = 7.333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 7.333333333 + 9 Reorder the terms: 9 + -6x + x2 = 7.333333333 + 9 Combine like terms: 7.333333333 + 9 = 16.333333333 9 + -6x + x2 = 16.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 16.333333333 Calculate the square root of the right side: 4.041451884 Break this problem into two subproblems by setting (x + -3) equal to 4.041451884 and -4.041451884.Subproblem 1
x + -3 = 4.041451884 Simplifying x + -3 = 4.041451884 Reorder the terms: -3 + x = 4.041451884 Solving -3 + x = 4.041451884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.041451884 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.041451884 + 3 x = 4.041451884 + 3 Combine like terms: 4.041451884 + 3 = 7.041451884 x = 7.041451884 Simplifying x = 7.041451884Subproblem 2
x + -3 = -4.041451884 Simplifying x + -3 = -4.041451884 Reorder the terms: -3 + x = -4.041451884 Solving -3 + x = -4.041451884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.041451884 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.041451884 + 3 x = -4.041451884 + 3 Combine like terms: -4.041451884 + 3 = -1.041451884 x = -1.041451884 Simplifying x = -1.041451884Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.041451884, -1.041451884}
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