3=(x-7)(x+5)

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Solution for 3=(x-7)(x+5) equation:


Simplifying
3 = (x + -7)(x + 5)

Reorder the terms:
3 = (-7 + x)(x + 5)

Reorder the terms:
3 = (-7 + x)(5 + x)

Multiply (-7 + x) * (5 + x)
3 = (-7(5 + x) + x(5 + x))
3 = ((5 * -7 + x * -7) + x(5 + x))
3 = ((-35 + -7x) + x(5 + x))
3 = (-35 + -7x + (5 * x + x * x))
3 = (-35 + -7x + (5x + x2))

Combine like terms: -7x + 5x = -2x
3 = (-35 + -2x + x2)

Solving
3 = -35 + -2x + x2

Solving for variable 'x'.

Combine like terms: 3 + 35 = 38
38 + 2x + -1x2 = -35 + -2x + x2 + 35 + 2x + -1x2

Reorder the terms:
38 + 2x + -1x2 = -35 + 35 + -2x + 2x + x2 + -1x2

Combine like terms: -35 + 35 = 0
38 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
38 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
38 + 2x + -1x2 = 0 + x2 + -1x2
38 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
38 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-38 + -2x + x2 = 0

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -2x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + -2x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -2x + x2 = 0 + 38
-2x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
-2x + x2 = 38

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 = 38 + 1

Reorder the terms:
1 + -2x + x2 = 38 + 1

Combine like terms: 38 + 1 = 39
1 + -2x + x2 = 39

Factor a perfect square on the left side:
(x + -1)(x + -1) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + -1) equal to 6.244997998 and -6.244997998.

Subproblem 1

x + -1 = 6.244997998 Simplifying x + -1 = 6.244997998 Reorder the terms: -1 + x = 6.244997998 Solving -1 + x = 6.244997998 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 = 6.244997998 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.244997998 + 1 x = 6.244997998 + 1 Combine like terms: 6.244997998 + 1 = 7.244997998 x = 7.244997998 Simplifying x = 7.244997998

Subproblem 2

x + -1 = -6.244997998 Simplifying x + -1 = -6.244997998 Reorder the terms: -1 + x = -6.244997998 Solving -1 + x = -6.244997998 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 = -6.244997998 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.244997998 + 1 x = -6.244997998 + 1 Combine like terms: -6.244997998 + 1 = -5.244997998 x = -5.244997998 Simplifying x = -5.244997998

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.244997998, -5.244997998}

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