x^2-8x-598=0

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Solution for x^2-8x-598=0 equation:


Simplifying
x2 + -8x + -598 = 0

Reorder the terms:
-598 + -8x + x2 = 0

Solving
-598 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '598' to each side of the equation.
-598 + -8x + 598 + x2 = 0 + 598

Reorder the terms:
-598 + 598 + -8x + x2 = 0 + 598

Combine like terms: -598 + 598 = 0
0 + -8x + x2 = 0 + 598
-8x + x2 = 0 + 598

Combine like terms: 0 + 598 = 598
-8x + x2 = 598

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 = 598 + 16

Reorder the terms:
16 + -8x + x2 = 598 + 16

Combine like terms: 598 + 16 = 614
16 + -8x + x2 = 614

Factor a perfect square on the left side:
(x + -4)(x + -4) = 614

Calculate the square root of the right side: 24.779023387

Break this problem into two subproblems by setting 
(x + -4) equal to 24.779023387 and -24.779023387.

Subproblem 1

x + -4 = 24.779023387 Simplifying x + -4 = 24.779023387 Reorder the terms: -4 + x = 24.779023387 Solving -4 + x = 24.779023387 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 = 24.779023387 + 4 Combine like terms: -4 + 4 = 0 0 + x = 24.779023387 + 4 x = 24.779023387 + 4 Combine like terms: 24.779023387 + 4 = 28.779023387 x = 28.779023387 Simplifying x = 28.779023387

Subproblem 2

x + -4 = -24.779023387 Simplifying x + -4 = -24.779023387 Reorder the terms: -4 + x = -24.779023387 Solving -4 + x = -24.779023387 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 = -24.779023387 + 4 Combine like terms: -4 + 4 = 0 0 + x = -24.779023387 + 4 x = -24.779023387 + 4 Combine like terms: -24.779023387 + 4 = -20.779023387 x = -20.779023387 Simplifying x = -20.779023387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28.779023387, -20.779023387}

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