x*x-5*x-5=0

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Solution for x*x-5*x-5=0 equation:


Simplifying
x * x + -5x + -5 = 0

Multiply x * x
x2 + -5x + -5 = 0

Reorder the terms:
-5 + -5x + x2 = 0

Solving
-5 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -5x + x2 = 0 + 5
-5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-5x + x2 = 5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + -5x + x2 = 11.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

x + -2.5 = 3.354101966 Simplifying x + -2.5 = 3.354101966 Reorder the terms: -2.5 + x = 3.354101966 Solving -2.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.354101966 + 2.5 x = 3.354101966 + 2.5 Combine like terms: 3.354101966 + 2.5 = 5.854101966 x = 5.854101966 Simplifying x = 5.854101966

Subproblem 2

x + -2.5 = -3.354101966 Simplifying x + -2.5 = -3.354101966 Reorder the terms: -2.5 + x = -3.354101966 Solving -2.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.354101966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.354101966 + 2.5 x = -3.354101966 + 2.5 Combine like terms: -3.354101966 + 2.5 = -0.854101966 x = -0.854101966 Simplifying x = -0.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.854101966, -0.854101966}

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