(x)(x+2)=28

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Solution for (x)(x+2)=28 equation:


Simplifying
(x)(x + 2) = 28

Reorder the terms:
x(2 + x) = 28
(2 * x + x * x) = 28
(2x + x2) = 28

Solving
2x + x2 = 28

Solving for variable 'x'.

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

Combine like terms: 28 + -28 = 0
-28 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 2x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 2x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 2x + x2 = 0 + 28
2x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
2x + x2 = 28

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 = 28 + 1

Reorder the terms:
1 + 2x + x2 = 28 + 1

Combine like terms: 28 + 1 = 29
1 + 2x + x2 = 29

Factor a perfect square on the left side:
(x + 1)(x + 1) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + 1) equal to 5.385164807 and -5.385164807.

Subproblem 1

x + 1 = 5.385164807 Simplifying x + 1 = 5.385164807 Reorder the terms: 1 + x = 5.385164807 Solving 1 + x = 5.385164807 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 = 5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.385164807 + -1 x = 5.385164807 + -1 Combine like terms: 5.385164807 + -1 = 4.385164807 x = 4.385164807 Simplifying x = 4.385164807

Subproblem 2

x + 1 = -5.385164807 Simplifying x + 1 = -5.385164807 Reorder the terms: 1 + x = -5.385164807 Solving 1 + x = -5.385164807 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 = -5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.385164807 + -1 x = -5.385164807 + -1 Combine like terms: -5.385164807 + -1 = -6.385164807 x = -6.385164807 Simplifying x = -6.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.385164807, -6.385164807}

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