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Simplifying 40(x) + (x + 2) = 9(x)(x + 2) Reorder the terms: 40x + (2 + x) = 9(x)(x + 2) Remove parenthesis around (2 + x) 40x + 2 + x = 9(x)(x + 2) Reorder the terms: 2 + 40x + x = 9(x)(x + 2) Combine like terms: 40x + x = 41x 2 + 41x = 9(x)(x + 2) Reorder the terms: 2 + 41x = 9x(2 + x) 2 + 41x = (2 * 9x + x * 9x) 2 + 41x = (18x + 9x2) Solving 2 + 41x = 18x + 9x2 Solving for variable 'x'. Combine like terms: 41x + -18x = 23x 2 + 23x + -9x2 = 18x + 9x2 + -18x + -9x2 Reorder the terms: 2 + 23x + -9x2 = 18x + -18x + 9x2 + -9x2 Combine like terms: 18x + -18x = 0 2 + 23x + -9x2 = 0 + 9x2 + -9x2 2 + 23x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 2 + 23x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.2222222222 + -2.555555556x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -2.555555556x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -2.555555556x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -2.555555556x + x2 = 0 + 0.2222222222 -2.555555556x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -2.555555556x + x2 = 0.2222222222 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 = 0.2222222222 + 1.632716050 Reorder the terms: 1.632716050 + -2.555555556x + x2 = 0.2222222222 + 1.632716050 Combine like terms: 0.2222222222 + 1.632716050 = 1.8549382722 1.632716050 + -2.555555556x + x2 = 1.8549382722 Factor a perfect square on the left side: (x + -1.277777778)(x + -1.277777778) = 1.8549382722 Calculate the square root of the right side: 1.361961186 Break this problem into two subproblems by setting (x + -1.277777778) equal to 1.361961186 and -1.361961186.Subproblem 1
x + -1.277777778 = 1.361961186 Simplifying x + -1.277777778 = 1.361961186 Reorder the terms: -1.277777778 + x = 1.361961186 Solving -1.277777778 + x = 1.361961186 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 = 1.361961186 + 1.277777778 Combine like terms: -1.277777778 + 1.277777778 = 0.000000000 0.000000000 + x = 1.361961186 + 1.277777778 x = 1.361961186 + 1.277777778 Combine like terms: 1.361961186 + 1.277777778 = 2.639738964 x = 2.639738964 Simplifying x = 2.639738964Subproblem 2
x + -1.277777778 = -1.361961186 Simplifying x + -1.277777778 = -1.361961186 Reorder the terms: -1.277777778 + x = -1.361961186 Solving -1.277777778 + x = -1.361961186 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 = -1.361961186 + 1.277777778 Combine like terms: -1.277777778 + 1.277777778 = 0.000000000 0.000000000 + x = -1.361961186 + 1.277777778 x = -1.361961186 + 1.277777778 Combine like terms: -1.361961186 + 1.277777778 = -0.084183408 x = -0.084183408 Simplifying x = -0.084183408Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.639738964, -0.084183408}
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