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Simplifying 9x2 + 23x + 6 = 0 Reorder the terms: 6 + 23x + 9x2 = 0 Solving 6 + 23x + 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'. 0.6666666667 + 2.555555556x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 2.555555556x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 2.555555556x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 2.555555556x + x2 = 0 + -0.6666666667 2.555555556x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 2.555555556x + x2 = -0.6666666667 The x term is 2.555555556x. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556x + 1.632716050 + x2 = -0.6666666667 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556x + x2 = -0.6666666667 + 1.632716050 Combine like terms: -0.6666666667 + 1.632716050 = 0.9660493833 1.632716050 + 2.555555556x + x2 = 0.9660493833 Factor a perfect square on the left side: (x + 1.277777778)(x + 1.277777778) = 0.9660493833 Calculate the square root of the right side: 0.982878112 Break this problem into two subproblems by setting (x + 1.277777778) equal to 0.982878112 and -0.982878112.Subproblem 1
x + 1.277777778 = 0.982878112 Simplifying x + 1.277777778 = 0.982878112 Reorder the terms: 1.277777778 + x = 0.982878112 Solving 1.277777778 + x = 0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = 0.982878112 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = 0.982878112 + -1.277777778 x = 0.982878112 + -1.277777778 Combine like terms: 0.982878112 + -1.277777778 = -0.294899666 x = -0.294899666 Simplifying x = -0.294899666Subproblem 2
x + 1.277777778 = -0.982878112 Simplifying x + 1.277777778 = -0.982878112 Reorder the terms: 1.277777778 + x = -0.982878112 Solving 1.277777778 + x = -0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = -0.982878112 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = -0.982878112 + -1.277777778 x = -0.982878112 + -1.277777778 Combine like terms: -0.982878112 + -1.277777778 = -2.26065589 x = -2.26065589 Simplifying x = -2.26065589Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.294899666, -2.26065589}
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