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Simplifying (x + 2)(x + -3) = (x + 3) Reorder the terms: (2 + x)(x + -3) = (x + 3) Reorder the terms: (2 + x)(-3 + x) = (x + 3) Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) = (x + 3) ((-3 * 2 + x * 2) + x(-3 + x)) = (x + 3) ((-6 + 2x) + x(-3 + x)) = (x + 3) (-6 + 2x + (-3 * x + x * x)) = (x + 3) (-6 + 2x + (-3x + x2)) = (x + 3) Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) = (x + 3) Reorder the terms: -6 + -1x + x2 = (3 + x) Remove parenthesis around (3 + x) -6 + -1x + x2 = 3 + x Solving -6 + -1x + x2 = 3 + x Solving for variable 'x'. Reorder the terms: -6 + -3 + -1x + -1x + x2 = 3 + x + -3 + -1x Combine like terms: -6 + -3 = -9 -9 + -1x + -1x + x2 = 3 + x + -3 + -1x Combine like terms: -1x + -1x = -2x -9 + -2x + x2 = 3 + x + -3 + -1x Reorder the terms: -9 + -2x + x2 = 3 + -3 + x + -1x Combine like terms: 3 + -3 = 0 -9 + -2x + x2 = 0 + x + -1x -9 + -2x + x2 = x + -1x Combine like terms: x + -1x = 0 -9 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x + x2 = 0 + 9 -2x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2x + x2 = 9 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 = 9 + 1 Reorder the terms: 1 + -2x + x2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2x + x2 = 10 Factor a perfect square on the left side: (x + -1)(x + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -1 = 3.16227766 Simplifying x + -1 = 3.16227766 Reorder the terms: -1 + x = 3.16227766 Solving -1 + x = 3.16227766 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 = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.16227766 + 1 x = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 x = 4.16227766 Simplifying x = 4.16227766Subproblem 2
x + -1 = -3.16227766 Simplifying x + -1 = -3.16227766 Reorder the terms: -1 + x = -3.16227766 Solving -1 + x = -3.16227766 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 = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.16227766 + 1 x = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 x = -2.16227766 Simplifying x = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.16227766, -2.16227766}
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