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Simplifying 0 = 3x2 + -22x + 6 Reorder the terms: 0 = 6 + -22x + 3x2 Solving 0 = 6 + -22x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + 22x + -3x2 = 6 + -22x + 3x2 + -6 + 22x + -3x2 Reorder the terms: -6 + 22x + -3x2 = 6 + -6 + -22x + 22x + 3x2 + -3x2 Combine like terms: 6 + -6 = 0 -6 + 22x + -3x2 = 0 + -22x + 22x + 3x2 + -3x2 -6 + 22x + -3x2 = -22x + 22x + 3x2 + -3x2 Combine like terms: -22x + 22x = 0 -6 + 22x + -3x2 = 0 + 3x2 + -3x2 -6 + 22x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + 22x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7.333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -7.333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7.333333333x + x2 = 0 + -2 -7.333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7.333333333x + x2 = -2 The x term is -7.333333333x. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333x + 13.44444445 + x2 = -2 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = -2 + 13.44444445 Combine like terms: -2 + 13.44444445 = 11.44444445 13.44444445 + -7.333333333x + x2 = 11.44444445 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 11.44444445 Calculate the square root of the right side: 3.382963856 Break this problem into two subproblems by setting (x + -3.666666667) equal to 3.382963856 and -3.382963856.Subproblem 1
x + -3.666666667 = 3.382963856 Simplifying x + -3.666666667 = 3.382963856 Reorder the terms: -3.666666667 + x = 3.382963856 Solving -3.666666667 + x = 3.382963856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = 3.382963856 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 3.382963856 + 3.666666667 x = 3.382963856 + 3.666666667 Combine like terms: 3.382963856 + 3.666666667 = 7.049630523 x = 7.049630523 Simplifying x = 7.049630523Subproblem 2
x + -3.666666667 = -3.382963856 Simplifying x + -3.666666667 = -3.382963856 Reorder the terms: -3.666666667 + x = -3.382963856 Solving -3.666666667 + x = -3.382963856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = -3.382963856 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -3.382963856 + 3.666666667 x = -3.382963856 + 3.666666667 Combine like terms: -3.382963856 + 3.666666667 = 0.283702811 x = 0.283702811 Simplifying x = 0.283702811Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.049630523, 0.283702811}
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