(x-7)(x+4)=2

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Solution for (x-7)(x+4)=2 equation:


Simplifying
(x + -7)(x + 4) = 2

Reorder the terms:
(-7 + x)(x + 4) = 2

Reorder the terms:
(-7 + x)(4 + x) = 2

Multiply (-7 + x) * (4 + x)
(-7(4 + x) + x(4 + x)) = 2
((4 * -7 + x * -7) + x(4 + x)) = 2
((-28 + -7x) + x(4 + x)) = 2
(-28 + -7x + (4 * x + x * x)) = 2
(-28 + -7x + (4x + x2)) = 2

Combine like terms: -7x + 4x = -3x
(-28 + -3x + x2) = 2

Solving
-28 + -3x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
-28 + -2 + -3x + x2 = 2 + -2

Combine like terms: -28 + -2 = -30
-30 + -3x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-30 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -3x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -3x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -3x + x2 = 0 + 30
-3x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-3x + x2 = 30

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 30 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + -3x + x2 = 32.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + -1.5 = 5.678908346 Simplifying x + -1.5 = 5.678908346 Reorder the terms: -1.5 + x = 5.678908346 Solving -1.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.678908346 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.678908346 + 1.5 x = 5.678908346 + 1.5 Combine like terms: 5.678908346 + 1.5 = 7.178908346 x = 7.178908346 Simplifying x = 7.178908346

Subproblem 2

x + -1.5 = -5.678908346 Simplifying x + -1.5 = -5.678908346 Reorder the terms: -1.5 + x = -5.678908346 Solving -1.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.678908346 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.678908346 + 1.5 x = -5.678908346 + 1.5 Combine like terms: -5.678908346 + 1.5 = -4.178908346 x = -4.178908346 Simplifying x = -4.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.178908346, -4.178908346}

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