x^2-8x-20=600

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Solution for x^2-8x-20=600 equation:


Simplifying
x2 + -8x + -20 = 600

Reorder the terms:
-20 + -8x + x2 = 600

Solving
-20 + -8x + x2 = 600

Solving for variable 'x'.

Reorder the terms:
-20 + -600 + -8x + x2 = 600 + -600

Combine like terms: -20 + -600 = -620
-620 + -8x + x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-620 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '620' to each side of the equation.
-620 + -8x + 620 + x2 = 0 + 620

Reorder the terms:
-620 + 620 + -8x + x2 = 0 + 620

Combine like terms: -620 + 620 = 0
0 + -8x + x2 = 0 + 620
-8x + x2 = 0 + 620

Combine like terms: 0 + 620 = 620
-8x + x2 = 620

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 620 + 16

Reorder the terms:
16 + -8x + x2 = 620 + 16

Combine like terms: 620 + 16 = 636
16 + -8x + x2 = 636

Factor a perfect square on the left side:
(x + -4)(x + -4) = 636

Calculate the square root of the right side: 25.219040426

Break this problem into two subproblems by setting 
(x + -4) equal to 25.219040426 and -25.219040426.

Subproblem 1

x + -4 = 25.219040426 Simplifying x + -4 = 25.219040426 Reorder the terms: -4 + x = 25.219040426 Solving -4 + x = 25.219040426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 25.219040426 + 4 Combine like terms: -4 + 4 = 0 0 + x = 25.219040426 + 4 x = 25.219040426 + 4 Combine like terms: 25.219040426 + 4 = 29.219040426 x = 29.219040426 Simplifying x = 29.219040426

Subproblem 2

x + -4 = -25.219040426 Simplifying x + -4 = -25.219040426 Reorder the terms: -4 + x = -25.219040426 Solving -4 + x = -25.219040426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -25.219040426 + 4 Combine like terms: -4 + 4 = 0 0 + x = -25.219040426 + 4 x = -25.219040426 + 4 Combine like terms: -25.219040426 + 4 = -21.219040426 x = -21.219040426 Simplifying x = -21.219040426

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.219040426, -21.219040426}

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