x^2-3x-2.25=22.25

Simple and best practice solution for x^2-3x-2.25=22.25 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^2-3x-2.25=22.25 equation: 


Simplifying
x2 + -3x + -2.25 = 22.25

Reorder the terms:
-2.25 + -3x + x2 = 22.25

Solving
-2.25 + -3x + x2 = 22.25

Solving for variable 'x'.

Reorder the terms:
-2.25 + -22.25 + -3x + x2 = 22.25 + -22.25

Combine like terms: -2.25 + -22.25 = -24.5
-24.5 + -3x + x2 = 22.25 + -22.25

Combine like terms: 22.25 + -22.25 = 0.00
-24.5 + -3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '24.5' to each side of the equation.
-24.5 + -3x + 24.5 + x2 = 0.00 + 24.5

Reorder the terms:
-24.5 + 24.5 + -3x + x2 = 0.00 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + -3x + x2 = 0.00 + 24.5
-3x + x2 = 0.00 + 24.5

Combine like terms: 0.00 + 24.5 = 24.5
-3x + x2 = 24.5

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 = 24.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 24.5 + 2.25

Combine like terms: 24.5 + 2.25 = 26.75
2.25 + -3x + x2 = 26.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 26.75

Calculate the square root of the right side: 5.172040216

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.172040216 and -5.172040216.


Subproblem 1
x + -1.5 = 5.172040216

Simplifying
x + -1.5 = 5.172040216

Reorder the terms:
-1.5 + x = 5.172040216

Solving
-1.5 + x = 5.172040216

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 = 5.172040216 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 5.172040216 + 1.5
x = 5.172040216 + 1.5

Combine like terms: 5.172040216 + 1.5 = 6.672040216
x = 6.672040216

Simplifying
x = 6.672040216


Subproblem 2
x + -1.5 = -5.172040216

Simplifying
x + -1.5 = -5.172040216

Reorder the terms:
-1.5 + x = -5.172040216

Solving
-1.5 + x = -5.172040216

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 = -5.172040216 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -5.172040216 + 1.5
x = -5.172040216 + 1.5

Combine like terms: -5.172040216 + 1.5 = -3.672040216
x = -3.672040216

Simplifying
x = -3.672040216


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.672040216, -3.672040216}

See similar equations:

| (4x^3/6y^5)^3 | | 5/12=x/420 | | x^2-5x-6.25=14.25 | | 0.45x=0.325 | | 3x-3(2x-11)=-3 | | 2x^2-14x+25=5 | | 17-y=23.75+-1.25y | | X+6.8=53.5 | | x/8-6=1 | | x^2-7x-12.25=16.25 | | 0=3x^2-3x-18 | | -3n-5=-3n-12 | | 6+x+5x+7= | | 11k+5=2k+1 | | 15c-18c-10c= | | 9y/1(1/3) | | 8(x-3)=25 | | 0=x^3+4x^2-12x | | 4xy(-3)=xy | | 7(x-4)=5(2x-6)-13 | | 5ln(2x+1)=55 | | -2(-x+1)=20 | | -124+4x=12x+76 | | 8-2(5x+5)=-2(1-4x) | | 20x+(15x+2)=205 | | x^2+2x+1=-8 | | 2(5x-8)+12=-2(9x-12) | | -21=9a-1513a | | Y=x^3+4x^2+3 | | -33=-8+-5y | | -(3+2a)+6a=4(a+4) | | Y=x^3+4c^2+3 |

Equations solver categories