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Simplifying (x + 4)(x + -5) = 4(x + -2) Reorder the terms: (4 + x)(x + -5) = 4(x + -2) Reorder the terms: (4 + x)(-5 + x) = 4(x + -2) Multiply (4 + x) * (-5 + x) (4(-5 + x) + x(-5 + x)) = 4(x + -2) ((-5 * 4 + x * 4) + x(-5 + x)) = 4(x + -2) ((-20 + 4x) + x(-5 + x)) = 4(x + -2) (-20 + 4x + (-5 * x + x * x)) = 4(x + -2) (-20 + 4x + (-5x + x2)) = 4(x + -2) Combine like terms: 4x + -5x = -1x (-20 + -1x + x2) = 4(x + -2) Reorder the terms: -20 + -1x + x2 = 4(-2 + x) -20 + -1x + x2 = (-2 * 4 + x * 4) -20 + -1x + x2 = (-8 + 4x) Solving -20 + -1x + x2 = -8 + 4x Solving for variable 'x'. Reorder the terms: -20 + 8 + -1x + -4x + x2 = -8 + 4x + 8 + -4x Combine like terms: -20 + 8 = -12 -12 + -1x + -4x + x2 = -8 + 4x + 8 + -4x Combine like terms: -1x + -4x = -5x -12 + -5x + x2 = -8 + 4x + 8 + -4x Reorder the terms: -12 + -5x + x2 = -8 + 8 + 4x + -4x Combine like terms: -8 + 8 = 0 -12 + -5x + x2 = 0 + 4x + -4x -12 + -5x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -12 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5x + x2 = 0 + 12 -5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -5x + x2 = 12 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 12 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + -5x + x2 = 18.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -2.5 = 4.272001873 Simplifying x + -2.5 = 4.272001873 Reorder the terms: -2.5 + x = 4.272001873 Solving -2.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.272001873 + 2.5 x = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 x = 6.772001873 Simplifying x = 6.772001873Subproblem 2
x + -2.5 = -4.272001873 Simplifying x + -2.5 = -4.272001873 Reorder the terms: -2.5 + x = -4.272001873 Solving -2.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.272001873 + 2.5 x = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 x = -1.772001873 Simplifying x = -1.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.772001873, -1.772001873}
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