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Simplifying 9x2 + 36x + 14 = 0 Reorder the terms: 14 + 36x + 9x2 = 0 Solving 14 + 36x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.555555556 + 4x + x2 = 0 Move the constant term to the right: Add '-1.555555556' to each side of the equation. 1.555555556 + 4x + -1.555555556 + x2 = 0 + -1.555555556 Reorder the terms: 1.555555556 + -1.555555556 + 4x + x2 = 0 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + 4x + x2 = 0 + -1.555555556 4x + x2 = 0 + -1.555555556 Combine like terms: 0 + -1.555555556 = -1.555555556 4x + x2 = -1.555555556 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.555555556 + 4 Reorder the terms: 4 + 4x + x2 = -1.555555556 + 4 Combine like terms: -1.555555556 + 4 = 2.444444444 4 + 4x + x2 = 2.444444444 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.444444444 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (x + 2) equal to 1.56347192 and -1.56347192.Subproblem 1
x + 2 = 1.56347192 Simplifying x + 2 = 1.56347192 Reorder the terms: 2 + x = 1.56347192 Solving 2 + x = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.56347192 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.56347192 + -2 x = 1.56347192 + -2 Combine like terms: 1.56347192 + -2 = -0.43652808 x = -0.43652808 Simplifying x = -0.43652808Subproblem 2
x + 2 = -1.56347192 Simplifying x + 2 = -1.56347192 Reorder the terms: 2 + x = -1.56347192 Solving 2 + x = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.56347192 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.56347192 + -2 x = -1.56347192 + -2 Combine like terms: -1.56347192 + -2 = -3.56347192 x = -3.56347192 Simplifying x = -3.56347192Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.43652808, -3.56347192}
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