x^2-16x-40=

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Solution for x^2-16x-40= equation:


Simplifying
x2 + -16x + -40 = 0

Reorder the terms:
-40 + -16x + x2 = 0

Solving
-40 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -16x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -16x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -16x + x2 = 0 + 40
-16x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-16x + x2 = 40

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 40 + 64

Reorder the terms:
64 + -16x + x2 = 40 + 64

Combine like terms: 40 + 64 = 104
64 + -16x + x2 = 104

Factor a perfect square on the left side:
(x + -8)(x + -8) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(x + -8) equal to 10.198039027 and -10.198039027.

Subproblem 1

x + -8 = 10.198039027 Simplifying x + -8 = 10.198039027 Reorder the terms: -8 + x = 10.198039027 Solving -8 + x = 10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 10.198039027 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.198039027 + 8 x = 10.198039027 + 8 Combine like terms: 10.198039027 + 8 = 18.198039027 x = 18.198039027 Simplifying x = 18.198039027

Subproblem 2

x + -8 = -10.198039027 Simplifying x + -8 = -10.198039027 Reorder the terms: -8 + x = -10.198039027 Solving -8 + x = -10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -10.198039027 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.198039027 + 8 x = -10.198039027 + 8 Combine like terms: -10.198039027 + 8 = -2.198039027 x = -2.198039027 Simplifying x = -2.198039027

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.198039027, -2.198039027}

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