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Simplifying 3x2 + -22x + 36 = 0 Reorder the terms: 36 + -22x + 3x2 = 0 Solving 36 + -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'. 12 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7.333333333x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -7.333333333x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7.333333333x + x2 = 0 + -12 -7.333333333x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7.333333333x + x2 = -12 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 = -12 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = -12 + 13.44444445 Combine like terms: -12 + 13.44444445 = 1.44444445 13.44444445 + -7.333333333x + x2 = 1.44444445 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 1.44444445 Calculate the square root of the right side: 1.201850427 Break this problem into two subproblems by setting (x + -3.666666667) equal to 1.201850427 and -1.201850427.Subproblem 1
x + -3.666666667 = 1.201850427 Simplifying x + -3.666666667 = 1.201850427 Reorder the terms: -3.666666667 + x = 1.201850427 Solving -3.666666667 + x = 1.201850427 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 = 1.201850427 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 1.201850427 + 3.666666667 x = 1.201850427 + 3.666666667 Combine like terms: 1.201850427 + 3.666666667 = 4.868517094 x = 4.868517094 Simplifying x = 4.868517094Subproblem 2
x + -3.666666667 = -1.201850427 Simplifying x + -3.666666667 = -1.201850427 Reorder the terms: -3.666666667 + x = -1.201850427 Solving -3.666666667 + x = -1.201850427 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 = -1.201850427 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -1.201850427 + 3.666666667 x = -1.201850427 + 3.666666667 Combine like terms: -1.201850427 + 3.666666667 = 2.46481624 x = 2.46481624 Simplifying x = 2.46481624Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.868517094, 2.46481624}
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