x^2+x+0.25=25

Simple and best practice solution for x^2+x+0.25=25 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2+x+0.25=25 equation: 


Simplifying
x2 + x + 0.25 = 25

Reorder the terms:
0.25 + x + x2 = 25

Solving
0.25 + x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
0.25 + -25 + x + x2 = 25 + -25

Combine like terms: 0.25 + -25 = -24.75
-24.75 + x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24.75 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24.75' to each side of the equation.
-24.75 + x + 24.75 + x2 = 0 + 24.75

Reorder the terms:
-24.75 + 24.75 + x + x2 = 0 + 24.75

Combine like terms: -24.75 + 24.75 = 0.00
0.00 + x + x2 = 0 + 24.75
x + x2 = 0 + 24.75

Combine like terms: 0 + 24.75 = 24.75
x + x2 = 24.75

The x term is x.  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.
x + 0.25 + x2 = 24.75 + 0.25

Reorder the terms:
0.25 + x + x2 = 24.75 + 0.25

Combine like terms: 24.75 + 0.25 = 25
0.25 + x + x2 = 25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5 and -5.


Subproblem 1
x + 0.5 = 5

Simplifying
x + 0.5 = 5

Reorder the terms:
0.5 + x = 5

Solving
0.5 + x = 5

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 = 5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5 + -0.5
x = 5 + -0.5

Combine like terms: 5 + -0.5 = 4.5
x = 4.5

Simplifying
x = 4.5


Subproblem 2
x + 0.5 = -5

Simplifying
x + 0.5 = -5

Reorder the terms:
0.5 + x = -5

Solving
0.5 + x = -5

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 = -5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5 + -0.5
x = -5 + -0.5

Combine like terms: -5 + -0.5 = -5.5
x = -5.5

Simplifying
x = -5.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5, -5.5}

See similar equations:

| 3x+5x+10x=180 | | 3/4t-4=2 | | 6=-2+4(p+8) | | y/2-1=2 | | x*x-2x-5=0 | | 28=-4x+8(2x-1) | | x/3=8.1 | | 2(x+1)-4=4x-2(2+x) | | 1+5n+5=10+3n | | 6(3n-3)=(8n+6)+2 | | 50x+3n=100 | | z^2+10z=75 | | 4=4-4y-7y | | y-1=-0.75(x-1) | | (224.9/0.2)^2/3 | | -9=.16z-11 | | 3+dz=12 | | 5x+9=x+11 | | -9h-6+12+40=22 | | 5x+9=x+111 | | 15y-10=14y+13 | | y-6=-1(x-2) | | y-4=-1.5(x-3) | | 3x-4y+1z+10=0 | | y=-4/3(1)-5 | | 3x/4-6=x/4-8 | | 25.6=w/8 | | 6x=7.68 | | 12/7x-3/5=5x/2+1/2 | | 3r^3+3-6r^4+2= | | 3r^3+-6r^4+2= | | Y=4X^4-8x^3+8X |

Equations solver categories