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Simplifying (x + 5) = (x + 9)(x + 2) Reorder the terms: (5 + x) = (x + 9)(x + 2) Remove parenthesis around (5 + x) 5 + x = (x + 9)(x + 2) Reorder the terms: 5 + x = (9 + x)(x + 2) Reorder the terms: 5 + x = (9 + x)(2 + x) Multiply (9 + x) * (2 + x) 5 + x = (9(2 + x) + x(2 + x)) 5 + x = ((2 * 9 + x * 9) + x(2 + x)) 5 + x = ((18 + 9x) + x(2 + x)) 5 + x = (18 + 9x + (2 * x + x * x)) 5 + x = (18 + 9x + (2x + x2)) Combine like terms: 9x + 2x = 11x 5 + x = (18 + 11x + x2) Solving 5 + x = 18 + 11x + x2 Solving for variable 'x'. Reorder the terms: 5 + -18 + x + -11x + -1x2 = 18 + 11x + x2 + -18 + -11x + -1x2 Combine like terms: 5 + -18 = -13 -13 + x + -11x + -1x2 = 18 + 11x + x2 + -18 + -11x + -1x2 Combine like terms: x + -11x = -10x -13 + -10x + -1x2 = 18 + 11x + x2 + -18 + -11x + -1x2 Reorder the terms: -13 + -10x + -1x2 = 18 + -18 + 11x + -11x + x2 + -1x2 Combine like terms: 18 + -18 = 0 -13 + -10x + -1x2 = 0 + 11x + -11x + x2 + -1x2 -13 + -10x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 -13 + -10x + -1x2 = 0 + x2 + -1x2 -13 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -13 + -10x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 10x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 10x + x2)' equal to zero and attempt to solve: Simplifying 13 + 10x + x2 = 0 Solving 13 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 10x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 10x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 10x + x2 = 0 + -13 10x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 10x + x2 = -13 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -13 + 25 Reorder the terms: 25 + 10x + x2 = -13 + 25 Combine like terms: -13 + 25 = 12 25 + 10x + x2 = 12 Factor a perfect square on the left side: (x + 5)(x + 5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 5) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 5 = 3.464101615 Simplifying x + 5 = 3.464101615 Reorder the terms: 5 + x = 3.464101615 Solving 5 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 3.464101615 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.464101615 + -5 x = 3.464101615 + -5 Combine like terms: 3.464101615 + -5 = -1.535898385 x = -1.535898385 Simplifying x = -1.535898385Subproblem 2
x + 5 = -3.464101615 Simplifying x + 5 = -3.464101615 Reorder the terms: 5 + x = -3.464101615 Solving 5 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -3.464101615 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.464101615 + -5 x = -3.464101615 + -5 Combine like terms: -3.464101615 + -5 = -8.464101615 x = -8.464101615 Simplifying x = -8.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.535898385, -8.464101615}Solution
x = {-1.535898385, -8.464101615}
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