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Simplifying 3x2 + 18x + 22 = 0 Reorder the terms: 22 + 18x + 3x2 = 0 Solving 22 + 18x + 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'. 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 = 1.666666667 9 + 6x + x2 = 1.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 1.666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (x + 3) equal to 1.290994449 and -1.290994449.Subproblem 1
x + 3 = 1.290994449 Simplifying x + 3 = 1.290994449 Reorder the terms: 3 + x = 1.290994449 Solving 3 + x = 1.290994449 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 = 1.290994449 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.290994449 + -3 x = 1.290994449 + -3 Combine like terms: 1.290994449 + -3 = -1.709005551 x = -1.709005551 Simplifying x = -1.709005551Subproblem 2
x + 3 = -1.290994449 Simplifying x + 3 = -1.290994449 Reorder the terms: 3 + x = -1.290994449 Solving 3 + x = -1.290994449 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 = -1.290994449 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.290994449 + -3 x = -1.290994449 + -3 Combine like terms: -1.290994449 + -3 = -4.290994449 x = -4.290994449 Simplifying x = -4.290994449Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.709005551, -4.290994449}
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