2x^2+4x-32=9

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Solution for 2x^2+4x-32=9 equation:


Simplifying
2x2 + 4x + -32 = 9

Reorder the terms:
-32 + 4x + 2x2 = 9

Solving
-32 + 4x + 2x2 = 9

Solving for variable 'x'.

Reorder the terms:
-32 + -9 + 4x + 2x2 = 9 + -9

Combine like terms: -32 + -9 = -41
-41 + 4x + 2x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-41 + 4x + 2x2 = 0

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

Divide each side by '2'.
-20.5 + 2x + x2 = 0

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + 2x + 20.5 + x2 = 0 + 20.5

Reorder the terms:
-20.5 + 20.5 + 2x + x2 = 0 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + 2x + x2 = 0 + 20.5
2x + x2 = 0 + 20.5

Combine like terms: 0 + 20.5 = 20.5
2x + x2 = 20.5

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 = 20.5 + 1

Reorder the terms:
1 + 2x + x2 = 20.5 + 1

Combine like terms: 20.5 + 1 = 21.5
1 + 2x + x2 = 21.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 21.5

Calculate the square root of the right side: 4.636809248

Break this problem into two subproblems by setting 
(x + 1) equal to 4.636809248 and -4.636809248.

Subproblem 1

x + 1 = 4.636809248 Simplifying x + 1 = 4.636809248 Reorder the terms: 1 + x = 4.636809248 Solving 1 + x = 4.636809248 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 = 4.636809248 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.636809248 + -1 x = 4.636809248 + -1 Combine like terms: 4.636809248 + -1 = 3.636809248 x = 3.636809248 Simplifying x = 3.636809248

Subproblem 2

x + 1 = -4.636809248 Simplifying x + 1 = -4.636809248 Reorder the terms: 1 + x = -4.636809248 Solving 1 + x = -4.636809248 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 = -4.636809248 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.636809248 + -1 x = -4.636809248 + -1 Combine like terms: -4.636809248 + -1 = -5.636809248 x = -5.636809248 Simplifying x = -5.636809248

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.636809248, -5.636809248}

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