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Simplifying x = (2x + 9)(1 + -10x) Reorder the terms: x = (9 + 2x)(1 + -10x) Multiply (9 + 2x) * (1 + -10x) x = (9(1 + -10x) + 2x * (1 + -10x)) x = ((1 * 9 + -10x * 9) + 2x * (1 + -10x)) x = ((9 + -90x) + 2x * (1 + -10x)) x = (9 + -90x + (1 * 2x + -10x * 2x)) x = (9 + -90x + (2x + -20x2)) Combine like terms: -90x + 2x = -88x x = (9 + -88x + -20x2) Solving x = 9 + -88x + -20x2 Solving for variable 'x'. Reorder the terms: -9 + x + 88x + 20x2 = 9 + -88x + -20x2 + -9 + 88x + 20x2 Combine like terms: x + 88x = 89x -9 + 89x + 20x2 = 9 + -88x + -20x2 + -9 + 88x + 20x2 Reorder the terms: -9 + 89x + 20x2 = 9 + -9 + -88x + 88x + -20x2 + 20x2 Combine like terms: 9 + -9 = 0 -9 + 89x + 20x2 = 0 + -88x + 88x + -20x2 + 20x2 -9 + 89x + 20x2 = -88x + 88x + -20x2 + 20x2 Combine like terms: -88x + 88x = 0 -9 + 89x + 20x2 = 0 + -20x2 + 20x2 -9 + 89x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -9 + 89x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + 4.45x + x2 = 0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 4.45x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 4.45x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 4.45x + x2 = 0 + 0.45 4.45x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 4.45x + x2 = 0.45 The x term is 4.45x. Take half its coefficient (2.225). Square it (4.950625) and add it to both sides. Add '4.950625' to each side of the equation. 4.45x + 4.950625 + x2 = 0.45 + 4.950625 Reorder the terms: 4.950625 + 4.45x + x2 = 0.45 + 4.950625 Combine like terms: 0.45 + 4.950625 = 5.400625 4.950625 + 4.45x + x2 = 5.400625 Factor a perfect square on the left side: (x + 2.225)(x + 2.225) = 5.400625 Calculate the square root of the right side: 2.323924482 Break this problem into two subproblems by setting (x + 2.225) equal to 2.323924482 and -2.323924482.Subproblem 1
x + 2.225 = 2.323924482 Simplifying x + 2.225 = 2.323924482 Reorder the terms: 2.225 + x = 2.323924482 Solving 2.225 + x = 2.323924482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.225' to each side of the equation. 2.225 + -2.225 + x = 2.323924482 + -2.225 Combine like terms: 2.225 + -2.225 = 0.000 0.000 + x = 2.323924482 + -2.225 x = 2.323924482 + -2.225 Combine like terms: 2.323924482 + -2.225 = 0.098924482 x = 0.098924482 Simplifying x = 0.098924482Subproblem 2
x + 2.225 = -2.323924482 Simplifying x + 2.225 = -2.323924482 Reorder the terms: 2.225 + x = -2.323924482 Solving 2.225 + x = -2.323924482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.225' to each side of the equation. 2.225 + -2.225 + x = -2.323924482 + -2.225 Combine like terms: 2.225 + -2.225 = 0.000 0.000 + x = -2.323924482 + -2.225 x = -2.323924482 + -2.225 Combine like terms: -2.323924482 + -2.225 = -4.548924482 x = -4.548924482 Simplifying x = -4.548924482Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.098924482, -4.548924482}
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