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Simplifying (x + -9)(x + 12) = x Reorder the terms: (-9 + x)(x + 12) = x Reorder the terms: (-9 + x)(12 + x) = x Multiply (-9 + x) * (12 + x) (-9(12 + x) + x(12 + x)) = x ((12 * -9 + x * -9) + x(12 + x)) = x ((-108 + -9x) + x(12 + x)) = x (-108 + -9x + (12 * x + x * x)) = x (-108 + -9x + (12x + x2)) = x Combine like terms: -9x + 12x = 3x (-108 + 3x + x2) = x Solving -108 + 3x + x2 = x Solving for variable 'x'. Reorder the terms: -108 + 3x + -1x + x2 = x + -1x Combine like terms: 3x + -1x = 2x -108 + 2x + x2 = x + -1x Combine like terms: x + -1x = 0 -108 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + 2x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 2x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 2x + x2 = 0 + 108 2x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 2x + x2 = 108 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 108 + 1 Reorder the terms: 1 + 2x + x2 = 108 + 1 Combine like terms: 108 + 1 = 109 1 + 2x + x2 = 109 Factor a perfect square on the left side: (x + 1)(x + 1) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 1) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 1 = 10.440306509 Simplifying x + 1 = 10.440306509 Reorder the terms: 1 + x = 10.440306509 Solving 1 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.440306509 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.440306509 + -1 x = 10.440306509 + -1 Combine like terms: 10.440306509 + -1 = 9.440306509 x = 9.440306509 Simplifying x = 9.440306509Subproblem 2
x + 1 = -10.440306509 Simplifying x + 1 = -10.440306509 Reorder the terms: 1 + x = -10.440306509 Solving 1 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.440306509 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.440306509 + -1 x = -10.440306509 + -1 Combine like terms: -10.440306509 + -1 = -11.440306509 x = -11.440306509 Simplifying x = -11.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.440306509, -11.440306509}
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