x^2-20x=16

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Solution for x^2-20x=16 equation:


Simplifying
x2 + -20x = 16

Reorder the terms:
-20x + x2 = 16

Solving
-20x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -20x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -20x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -20x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -20x + x2 = 0 + 16
-20x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-20x + x2 = 16

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 16 + 100

Reorder the terms:
100 + -20x + x2 = 16 + 100

Combine like terms: 16 + 100 = 116
100 + -20x + x2 = 116

Factor a perfect square on the left side:
(x + -10)(x + -10) = 116

Calculate the square root of the right side: 10.770329614

Break this problem into two subproblems by setting 
(x + -10) equal to 10.770329614 and -10.770329614.

Subproblem 1

x + -10 = 10.770329614 Simplifying x + -10 = 10.770329614 Reorder the terms: -10 + x = 10.770329614 Solving -10 + x = 10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.770329614 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.770329614 + 10 x = 10.770329614 + 10 Combine like terms: 10.770329614 + 10 = 20.770329614 x = 20.770329614 Simplifying x = 20.770329614

Subproblem 2

x + -10 = -10.770329614 Simplifying x + -10 = -10.770329614 Reorder the terms: -10 + x = -10.770329614 Solving -10 + x = -10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.770329614 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.770329614 + 10 x = -10.770329614 + 10 Combine like terms: -10.770329614 + 10 = -0.770329614 x = -0.770329614 Simplifying x = -0.770329614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.770329614, -0.770329614}

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