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Simplifying (x + 2)(x + -3) + -5(x + 3) = 0 Reorder the terms: (2 + x)(x + -3) + -5(x + 3) = 0 Reorder the terms: (2 + x)(-3 + x) + -5(x + 3) = 0 Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) + -5(x + 3) = 0 ((-3 * 2 + x * 2) + x(-3 + x)) + -5(x + 3) = 0 ((-6 + 2x) + x(-3 + x)) + -5(x + 3) = 0 (-6 + 2x + (-3 * x + x * x)) + -5(x + 3) = 0 (-6 + 2x + (-3x + x2)) + -5(x + 3) = 0 Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) + -5(x + 3) = 0 Reorder the terms: -6 + -1x + x2 + -5(3 + x) = 0 -6 + -1x + x2 + (3 * -5 + x * -5) = 0 -6 + -1x + x2 + (-15 + -5x) = 0 Reorder the terms: -6 + -15 + -1x + -5x + x2 = 0 Combine like terms: -6 + -15 = -21 -21 + -1x + -5x + x2 = 0 Combine like terms: -1x + -5x = -6x -21 + -6x + x2 = 0 Solving -21 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -6x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -6x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -6x + x2 = 0 + 21 -6x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -6x + x2 = 21 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 = 21 + 9 Reorder the terms: 9 + -6x + x2 = 21 + 9 Combine like terms: 21 + 9 = 30 9 + -6x + x2 = 30 Factor a perfect square on the left side: (x + -3)(x + -3) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -3) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -3 = 5.477225575 Simplifying x + -3 = 5.477225575 Reorder the terms: -3 + x = 5.477225575 Solving -3 + x = 5.477225575 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 = 5.477225575 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.477225575 + 3 x = 5.477225575 + 3 Combine like terms: 5.477225575 + 3 = 8.477225575 x = 8.477225575 Simplifying x = 8.477225575Subproblem 2
x + -3 = -5.477225575 Simplifying x + -3 = -5.477225575 Reorder the terms: -3 + x = -5.477225575 Solving -3 + x = -5.477225575 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 = -5.477225575 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.477225575 + 3 x = -5.477225575 + 3 Combine like terms: -5.477225575 + 3 = -2.477225575 x = -2.477225575 Simplifying x = -2.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.477225575, -2.477225575}
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