x^2-40x-9=0

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Solution for x^2-40x-9=0 equation:


Simplifying
x2 + -40x + -9 = 0

Reorder the terms:
-9 + -40x + x2 = 0

Solving
-9 + -40x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -40x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -40x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -40x + x2 = 0 + 9
-40x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-40x + x2 = 9

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 9 + 400

Reorder the terms:
400 + -40x + x2 = 9 + 400

Combine like terms: 9 + 400 = 409
400 + -40x + x2 = 409

Factor a perfect square on the left side:
(x + -20)(x + -20) = 409

Calculate the square root of the right side: 20.223748416

Break this problem into two subproblems by setting 
(x + -20) equal to 20.223748416 and -20.223748416.

Subproblem 1

x + -20 = 20.223748416 Simplifying x + -20 = 20.223748416 Reorder the terms: -20 + x = 20.223748416 Solving -20 + x = 20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 20.223748416 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.223748416 + 20 x = 20.223748416 + 20 Combine like terms: 20.223748416 + 20 = 40.223748416 x = 40.223748416 Simplifying x = 40.223748416

Subproblem 2

x + -20 = -20.223748416 Simplifying x + -20 = -20.223748416 Reorder the terms: -20 + x = -20.223748416 Solving -20 + x = -20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -20.223748416 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.223748416 + 20 x = -20.223748416 + 20 Combine like terms: -20.223748416 + 20 = -0.223748416 x = -0.223748416 Simplifying x = -0.223748416

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.223748416, -0.223748416}

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