x^2+3x+2.25=5

Simple and best practice solution for x^2+3x+2.25=5 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+3x+2.25=5 equation:


Simplifying
x2 + 3x + 2.25 = 5

Reorder the terms:
2.25 + 3x + x2 = 5

Solving
2.25 + 3x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
2.25 + -5 + 3x + x2 = 5 + -5

Combine like terms: 2.25 + -5 = -2.75
-2.75 + 3x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-2.75 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 3x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 3x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 3x + x2 = 0 + 2.75
3x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
3x + x2 = 2.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.75 + 2.25

Combine like terms: 2.75 + 2.25 = 5
2.25 + 3x + x2 = 5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + 1.5 = 2.236067978

Simplifying
x + 1.5 = 2.236067978

Reorder the terms:
1.5 + x = 2.236067978

Solving
1.5 + x = 2.236067978

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.236067978 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.236067978 + -1.5
x = 2.236067978 + -1.5

Combine like terms: 2.236067978 + -1.5 = 0.736067978
x = 0.736067978

Simplifying
x = 0.736067978


Subproblem 2
x + 1.5 = -2.236067978

Simplifying
x + 1.5 = -2.236067978

Reorder the terms:
1.5 + x = -2.236067978

Solving
1.5 + x = -2.236067978

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.236067978 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.236067978 + -1.5
x = -2.236067978 + -1.5

Combine like terms: -2.236067978 + -1.5 = -3.736067978
x = -3.736067978

Simplifying
x = -3.736067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.736067978, -3.736067978}

See similar equations:

| 6(3a+2)=10a+12 | | w/5=12 | | 100=z+(z*0.005) | | 11+3m=7m-4m+11 | | 12=r/9 | | c+5=3(c-1) | | (2a+9)^1/2-a+3=0 | | 2x+5y-7= | | w-143.5=5.6 | | -15=5(3q-10)1-5q | | 8x+x+49=0 | | 2x-6y=3 | | 4x^2-11x+17=5x+10 | | 32.5=v-9 | | X+45+2x= | | 6x^2-36x-49=0 | | 4444+333= | | 14.1-0.3x=1.3x-42 | | 2x+(13)y=67 | | 3u^2-3u-1=0 | | x-16=7.2 | | 9(m-2)=m+4 | | 5*x-18-4x=-36 | | 3xy-9y=0 | | 2a+9^1/2-a+3=0 | | t/1.2=0.9 | | -16=48 | | (v+3)(v-3)=8v | | -32+72r=14r-77r | | x^2+3x-2-1/2x^2+13/2=0 | | 2-2(-2n+5)=(7n-6)+7 | | -3(2x+1)=-15 |

Equations solver categories