0.25x^2+2x+4=0

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Solution for 0.25x^2+2x+4=0 equation:


Simplifying
0.25x2 + 2x + 4 = 0

Reorder the terms:
4 + 2x + 0.25x2 = 0

Solving
4 + 2x + 0.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.25 the coefficient of the squared term: 

Divide each side by '0.25'.
16 + 8x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 8x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 8x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 8x + x2 = 0 + -16
8x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
8x + x2 = -16

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 = -16 + 16

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

Combine like terms: -16 + 16 = 0
16 + 8x + x2 = 0

Factor a perfect square on the left side:
(x + 4)(x + 4) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + 4) equal to 0 and 0.

Subproblem 1

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

Subproblem 2

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

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4, -4}

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