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Simplifying 6x2 + 55x + -9 = 0 Reorder the terms: -9 + 55x + 6x2 = 0 Solving -9 + 55x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + 9.166666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 9.166666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 9.166666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 9.166666667x + x2 = 0 + 1.5 9.166666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 9.166666667x + x2 = 1.5 The x term is 9.166666667x. Take half its coefficient (4.583333334). Square it (21.00694445) and add it to both sides. Add '21.00694445' to each side of the equation. 9.166666667x + 21.00694445 + x2 = 1.5 + 21.00694445 Reorder the terms: 21.00694445 + 9.166666667x + x2 = 1.5 + 21.00694445 Combine like terms: 1.5 + 21.00694445 = 22.50694445 21.00694445 + 9.166666667x + x2 = 22.50694445 Factor a perfect square on the left side: (x + 4.583333334)(x + 4.583333334) = 22.50694445 Calculate the square root of the right side: 4.744148443 Break this problem into two subproblems by setting (x + 4.583333334) equal to 4.744148443 and -4.744148443.Subproblem 1
x + 4.583333334 = 4.744148443 Simplifying x + 4.583333334 = 4.744148443 Reorder the terms: 4.583333334 + x = 4.744148443 Solving 4.583333334 + x = 4.744148443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.583333334' to each side of the equation. 4.583333334 + -4.583333334 + x = 4.744148443 + -4.583333334 Combine like terms: 4.583333334 + -4.583333334 = 0.000000000 0.000000000 + x = 4.744148443 + -4.583333334 x = 4.744148443 + -4.583333334 Combine like terms: 4.744148443 + -4.583333334 = 0.160815109 x = 0.160815109 Simplifying x = 0.160815109Subproblem 2
x + 4.583333334 = -4.744148443 Simplifying x + 4.583333334 = -4.744148443 Reorder the terms: 4.583333334 + x = -4.744148443 Solving 4.583333334 + x = -4.744148443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.583333334' to each side of the equation. 4.583333334 + -4.583333334 + x = -4.744148443 + -4.583333334 Combine like terms: 4.583333334 + -4.583333334 = 0.000000000 0.000000000 + x = -4.744148443 + -4.583333334 x = -4.744148443 + -4.583333334 Combine like terms: -4.744148443 + -4.583333334 = -9.327481777 x = -9.327481777 Simplifying x = -9.327481777Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.160815109, -9.327481777}
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