x^2-x-174=0

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Solution for x^2-x-174=0 equation:


Simplifying
x2 + -1x + -174 = 0

Reorder the terms:
-174 + -1x + x2 = 0

Solving
-174 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '174' to each side of the equation.
-174 + -1x + 174 + x2 = 0 + 174

Reorder the terms:
-174 + 174 + -1x + x2 = 0 + 174

Combine like terms: -174 + 174 = 0
0 + -1x + x2 = 0 + 174
-1x + x2 = 0 + 174

Combine like terms: 0 + 174 = 174
-1x + x2 = 174

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 174 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 174 + 0.25

Combine like terms: 174 + 0.25 = 174.25
0.25 + -1x + x2 = 174.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 174.25

Calculate the square root of the right side: 13.200378782

Break this problem into two subproblems by setting 
(x + -0.5) equal to 13.200378782 and -13.200378782.

Subproblem 1

x + -0.5 = 13.200378782 Simplifying x + -0.5 = 13.200378782 Reorder the terms: -0.5 + x = 13.200378782 Solving -0.5 + x = 13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 13.200378782 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 13.200378782 + 0.5 x = 13.200378782 + 0.5 Combine like terms: 13.200378782 + 0.5 = 13.700378782 x = 13.700378782 Simplifying x = 13.700378782

Subproblem 2

x + -0.5 = -13.200378782 Simplifying x + -0.5 = -13.200378782 Reorder the terms: -0.5 + x = -13.200378782 Solving -0.5 + x = -13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -13.200378782 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -13.200378782 + 0.5 x = -13.200378782 + 0.5 Combine like terms: -13.200378782 + 0.5 = -12.700378782 x = -12.700378782 Simplifying x = -12.700378782

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.700378782, -12.700378782}

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