(X+2)(X-9)=24

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Solution for (X+2)(X-9)=24 equation:


Simplifying
(X + 2)(X + -9) = 24

Reorder the terms:
(2 + X)(X + -9) = 24

Reorder the terms:
(2 + X)(-9 + X) = 24

Multiply (2 + X) * (-9 + X)
(2(-9 + X) + X(-9 + X)) = 24
((-9 * 2 + X * 2) + X(-9 + X)) = 24
((-18 + 2X) + X(-9 + X)) = 24
(-18 + 2X + (-9 * X + X * X)) = 24
(-18 + 2X + (-9X + X2)) = 24

Combine like terms: 2X + -9X = -7X
(-18 + -7X + X2) = 24

Solving
-18 + -7X + X2 = 24

Solving for variable 'X'.

Reorder the terms:
-18 + -24 + -7X + X2 = 24 + -24

Combine like terms: -18 + -24 = -42
-42 + -7X + X2 = 24 + -24

Combine like terms: 24 + -24 = 0
-42 + -7X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -7X + 42 + X2 = 0 + 42

Reorder the terms:
-42 + 42 + -7X + X2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -7X + X2 = 0 + 42
-7X + X2 = 0 + 42

Combine like terms: 0 + 42 = 42
-7X + X2 = 42

The X term is -7X.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7X + 12.25 + X2 = 42 + 12.25

Reorder the terms:
12.25 + -7X + X2 = 42 + 12.25

Combine like terms: 42 + 12.25 = 54.25
12.25 + -7X + X2 = 54.25

Factor a perfect square on the left side:
(X + -3.5)(X + -3.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(X + -3.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

X + -3.5 = 7.365459931 Simplifying X + -3.5 = 7.365459931 Reorder the terms: -3.5 + X = 7.365459931 Solving -3.5 + X = 7.365459931 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = 7.365459931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = 7.365459931 + 3.5 X = 7.365459931 + 3.5 Combine like terms: 7.365459931 + 3.5 = 10.865459931 X = 10.865459931 Simplifying X = 10.865459931

Subproblem 2

X + -3.5 = -7.365459931 Simplifying X + -3.5 = -7.365459931 Reorder the terms: -3.5 + X = -7.365459931 Solving -3.5 + X = -7.365459931 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = -7.365459931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = -7.365459931 + 3.5 X = -7.365459931 + 3.5 Combine like terms: -7.365459931 + 3.5 = -3.865459931 X = -3.865459931 Simplifying X = -3.865459931

Solution

The solution to the problem is based on the solutions from the subproblems. X = {10.865459931, -3.865459931}

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