(x+3)(x-4)=6

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Solution for (x+3)(x-4)=6 equation:


Simplifying
(x + 3)(x + -4) = 6

Reorder the terms:
(3 + x)(x + -4) = 6

Reorder the terms:
(3 + x)(-4 + x) = 6

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = 6
((-4 * 3 + x * 3) + x(-4 + x)) = 6
((-12 + 3x) + x(-4 + x)) = 6
(-12 + 3x + (-4 * x + x * x)) = 6
(-12 + 3x + (-4x + x2)) = 6

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = 6

Solving
-12 + -1x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-12 + -6 + -1x + x2 = 6 + -6

Combine like terms: -12 + -6 = -18
-18 + -1x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-18 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -1x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x + x2 = 0 + 18
-1x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-1x + x2 = 18

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 18 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 18 + 0.25

Combine like terms: 18 + 0.25 = 18.25
0.25 + -1x + x2 = 18.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + -0.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + -0.5 = 4.272001873 Simplifying x + -0.5 = 4.272001873 Reorder the terms: -0.5 + x = 4.272001873 Solving -0.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.272001873 + 0.5 x = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 x = 4.772001873 Simplifying x = 4.772001873

Subproblem 2

x + -0.5 = -4.272001873 Simplifying x + -0.5 = -4.272001873 Reorder the terms: -0.5 + x = -4.272001873 Solving -0.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.272001873 + 0.5 x = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 x = -3.772001873 Simplifying x = -3.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.772001873, -3.772001873}

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