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Simplifying 3x2 + 22x + -6 = 0 Reorder the terms: -6 + 22x + 3x2 = 0 Solving -6 + 22x + 3x2 = 0 Solving for variable 'x'. 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 = 15.44444445 13.44444445 + 7.333333333x + x2 = 15.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 15.44444445 Calculate the square root of the right side: 3.929942042 Break this problem into two subproblems by setting (x + 3.666666667) equal to 3.929942042 and -3.929942042.Subproblem 1
x + 3.666666667 = 3.929942042 Simplifying x + 3.666666667 = 3.929942042 Reorder the terms: 3.666666667 + x = 3.929942042 Solving 3.666666667 + x = 3.929942042 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 = 3.929942042 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 3.929942042 + -3.666666667 x = 3.929942042 + -3.666666667 Combine like terms: 3.929942042 + -3.666666667 = 0.263275375 x = 0.263275375 Simplifying x = 0.263275375Subproblem 2
x + 3.666666667 = -3.929942042 Simplifying x + 3.666666667 = -3.929942042 Reorder the terms: 3.666666667 + x = -3.929942042 Solving 3.666666667 + x = -3.929942042 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 = -3.929942042 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -3.929942042 + -3.666666667 x = -3.929942042 + -3.666666667 Combine like terms: -3.929942042 + -3.666666667 = -7.596608709 x = -7.596608709 Simplifying x = -7.596608709Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.263275375, -7.596608709}
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