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Simplifying (x + 9)(x + -1) = (x + 3) * 2 Reorder the terms: (9 + x)(x + -1) = (x + 3) * 2 Reorder the terms: (9 + x)(-1 + x) = (x + 3) * 2 Multiply (9 + x) * (-1 + x) (9(-1 + x) + x(-1 + x)) = (x + 3) * 2 ((-1 * 9 + x * 9) + x(-1 + x)) = (x + 3) * 2 ((-9 + 9x) + x(-1 + x)) = (x + 3) * 2 (-9 + 9x + (-1 * x + x * x)) = (x + 3) * 2 (-9 + 9x + (-1x + x2)) = (x + 3) * 2 Combine like terms: 9x + -1x = 8x (-9 + 8x + x2) = (x + 3) * 2 Reorder the terms: -9 + 8x + x2 = (3 + x) * 2 Reorder the terms for easier multiplication: -9 + 8x + x2 = 2(3 + x) -9 + 8x + x2 = (3 * 2 + x * 2) -9 + 8x + x2 = (6 + 2x) Solving -9 + 8x + x2 = 6 + 2x Solving for variable 'x'. Reorder the terms: -9 + -6 + 8x + -2x + x2 = 6 + 2x + -6 + -2x Combine like terms: -9 + -6 = -15 -15 + 8x + -2x + x2 = 6 + 2x + -6 + -2x Combine like terms: 8x + -2x = 6x -15 + 6x + x2 = 6 + 2x + -6 + -2x Reorder the terms: -15 + 6x + x2 = 6 + -6 + 2x + -2x Combine like terms: 6 + -6 = 0 -15 + 6x + x2 = 0 + 2x + -2x -15 + 6x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -15 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 6x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 6x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6x + x2 = 0 + 15 6x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 6x + x2 = 15 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 15 + 9 Reorder the terms: 9 + 6x + x2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + 6x + x2 = 24 Factor a perfect square on the left side: (x + 3)(x + 3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 3) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 3 = 4.898979486 Simplifying x + 3 = 4.898979486 Reorder the terms: 3 + x = 4.898979486 Solving 3 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.898979486 + -3 x = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 x = 1.898979486 Simplifying x = 1.898979486Subproblem 2
x + 3 = -4.898979486 Simplifying x + 3 = -4.898979486 Reorder the terms: 3 + x = -4.898979486 Solving 3 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.898979486 + -3 x = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 x = -7.898979486 Simplifying x = -7.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.898979486, -7.898979486}
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