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Simplifying (9x + -1)(2x + 1) = 6x Reorder the terms: (-1 + 9x)(2x + 1) = 6x Reorder the terms: (-1 + 9x)(1 + 2x) = 6x Multiply (-1 + 9x) * (1 + 2x) (-1(1 + 2x) + 9x * (1 + 2x)) = 6x ((1 * -1 + 2x * -1) + 9x * (1 + 2x)) = 6x ((-1 + -2x) + 9x * (1 + 2x)) = 6x (-1 + -2x + (1 * 9x + 2x * 9x)) = 6x (-1 + -2x + (9x + 18x2)) = 6x Combine like terms: -2x + 9x = 7x (-1 + 7x + 18x2) = 6x Solving -1 + 7x + 18x2 = 6x Solving for variable 'x'. Reorder the terms: -1 + 7x + -6x + 18x2 = 6x + -6x Combine like terms: 7x + -6x = 1x -1 + 1x + 18x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -1 + 1x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 0.05555555556x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 0.05555555556x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 0.05555555556x + x2 = 0 + 0.05555555556 0.05555555556x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 0.05555555556x + x2 = 0.05555555556 The x term is 0.05555555556x. Take half its coefficient (0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. 0.05555555556x + 0.0007716049384 + x2 = 0.05555555556 + 0.0007716049384 Reorder the terms: 0.0007716049384 + 0.05555555556x + x2 = 0.05555555556 + 0.0007716049384 Combine like terms: 0.05555555556 + 0.0007716049384 = 0.0563271604984 0.0007716049384 + 0.05555555556x + x2 = 0.0563271604984 Factor a perfect square on the left side: (x + 0.02777777778)(x + 0.02777777778) = 0.0563271604984 Calculate the square root of the right side: 0.237333437 Break this problem into two subproblems by setting (x + 0.02777777778) equal to 0.237333437 and -0.237333437.Subproblem 1
x + 0.02777777778 = 0.237333437 Simplifying x + 0.02777777778 = 0.237333437 Reorder the terms: 0.02777777778 + x = 0.237333437 Solving 0.02777777778 + x = 0.237333437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = 0.237333437 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = 0.237333437 + -0.02777777778 x = 0.237333437 + -0.02777777778 Combine like terms: 0.237333437 + -0.02777777778 = 0.20955565922 x = 0.20955565922 Simplifying x = 0.20955565922Subproblem 2
x + 0.02777777778 = -0.237333437 Simplifying x + 0.02777777778 = -0.237333437 Reorder the terms: 0.02777777778 + x = -0.237333437 Solving 0.02777777778 + x = -0.237333437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02777777778' to each side of the equation. 0.02777777778 + -0.02777777778 + x = -0.237333437 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + x = -0.237333437 + -0.02777777778 x = -0.237333437 + -0.02777777778 Combine like terms: -0.237333437 + -0.02777777778 = -0.26511121478 x = -0.26511121478 Simplifying x = -0.26511121478Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.20955565922, -0.26511121478}
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