(x+7)(x-3)=21

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Solution for (x+7)(x-3)=21 equation:


Simplifying
(x + 7)(x + -3) = 21

Reorder the terms:
(7 + x)(x + -3) = 21

Reorder the terms:
(7 + x)(-3 + x) = 21

Multiply (7 + x) * (-3 + x)
(7(-3 + x) + x(-3 + x)) = 21
((-3 * 7 + x * 7) + x(-3 + x)) = 21
((-21 + 7x) + x(-3 + x)) = 21
(-21 + 7x + (-3 * x + x * x)) = 21
(-21 + 7x + (-3x + x2)) = 21

Combine like terms: 7x + -3x = 4x
(-21 + 4x + x2) = 21

Solving
-21 + 4x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -21 + 4x + x2 = 21 + -21

Combine like terms: -21 + -21 = -42
-42 + 4x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-42 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 4x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 4x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 4x + x2 = 0 + 42
4x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
4x + x2 = 42

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 42 + 4

Reorder the terms:
4 + 4x + x2 = 42 + 4

Combine like terms: 42 + 4 = 46
4 + 4x + x2 = 46

Factor a perfect square on the left side:
(x + 2)(x + 2) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 2) equal to 6.782329983 and -6.782329983.

Subproblem 1

x + 2 = 6.782329983 Simplifying x + 2 = 6.782329983 Reorder the terms: 2 + x = 6.782329983 Solving 2 + x = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.782329983 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.782329983 + -2 x = 6.782329983 + -2 Combine like terms: 6.782329983 + -2 = 4.782329983 x = 4.782329983 Simplifying x = 4.782329983

Subproblem 2

x + 2 = -6.782329983 Simplifying x + 2 = -6.782329983 Reorder the terms: 2 + x = -6.782329983 Solving 2 + x = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.782329983 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.782329983 + -2 x = -6.782329983 + -2 Combine like terms: -6.782329983 + -2 = -8.782329983 x = -8.782329983 Simplifying x = -8.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.782329983, -8.782329983}

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