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Simplifying 9x2 + 6x + -47 = 0 Reorder the terms: -47 + 6x + 9x2 = 0 Solving -47 + 6x + 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'. -5.222222222 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '5.222222222' to each side of the equation. -5.222222222 + 0.6666666667x + 5.222222222 + x2 = 0 + 5.222222222 Reorder the terms: -5.222222222 + 5.222222222 + 0.6666666667x + x2 = 0 + 5.222222222 Combine like terms: -5.222222222 + 5.222222222 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 5.222222222 0.6666666667x + x2 = 0 + 5.222222222 Combine like terms: 0 + 5.222222222 = 5.222222222 0.6666666667x + x2 = 5.222222222 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 5.222222222 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 5.222222222 + 0.1111111112 Combine like terms: 5.222222222 + 0.1111111112 = 5.3333333332 0.1111111112 + 0.6666666667x + x2 = 5.3333333332 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 5.3333333332 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 2.309401077 and -2.309401077.Subproblem 1
x + 0.3333333334 = 2.309401077 Simplifying x + 0.3333333334 = 2.309401077 Reorder the terms: 0.3333333334 + x = 2.309401077 Solving 0.3333333334 + x = 2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 2.309401077 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 2.309401077 + -0.3333333334 x = 2.309401077 + -0.3333333334 Combine like terms: 2.309401077 + -0.3333333334 = 1.9760677436 x = 1.9760677436 Simplifying x = 1.9760677436Subproblem 2
x + 0.3333333334 = -2.309401077 Simplifying x + 0.3333333334 = -2.309401077 Reorder the terms: 0.3333333334 + x = -2.309401077 Solving 0.3333333334 + x = -2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -2.309401077 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -2.309401077 + -0.3333333334 x = -2.309401077 + -0.3333333334 Combine like terms: -2.309401077 + -0.3333333334 = -2.6427344104 x = -2.6427344104 Simplifying x = -2.6427344104Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9760677436, -2.6427344104}
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