x*x+5x-5=0

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Solution for x*x+5x-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 = 0.854101966 x = 0.854101966 Simplifying x = 0.854101966

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 = -5.854101966 x = -5.854101966 Simplifying x = -5.854101966

Solution

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

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