x^2-4x-38=-8

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Solution for x^2-4x-38=-8 equation:


Simplifying
x2 + -4x + -38 = -8

Reorder the terms:
-38 + -4x + x2 = -8

Solving
-38 + -4x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-38 + 8 + -4x + x2 = -8 + 8

Combine like terms: -38 + 8 = -30
-30 + -4x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-30 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -4x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -4x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -4x + x2 = 0 + 30
-4x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-4x + x2 = 30

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 = 30 + 4

Reorder the terms:
4 + -4x + x2 = 30 + 4

Combine like terms: 30 + 4 = 34
4 + -4x + x2 = 34

Factor a perfect square on the left side:
(x + -2)(x + -2) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -2) equal to 5.830951895 and -5.830951895.

Subproblem 1

x + -2 = 5.830951895 Simplifying x + -2 = 5.830951895 Reorder the terms: -2 + x = 5.830951895 Solving -2 + x = 5.830951895 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 = 5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.830951895 + 2 x = 5.830951895 + 2 Combine like terms: 5.830951895 + 2 = 7.830951895 x = 7.830951895 Simplifying x = 7.830951895

Subproblem 2

x + -2 = -5.830951895 Simplifying x + -2 = -5.830951895 Reorder the terms: -2 + x = -5.830951895 Solving -2 + x = -5.830951895 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 = -5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.830951895 + 2 x = -5.830951895 + 2 Combine like terms: -5.830951895 + 2 = -3.830951895 x = -3.830951895 Simplifying x = -3.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.830951895, -3.830951895}

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