3x^2-5x-2.25=0

Simple and best practice solution for 3x^2-5x-2.25=0 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 3x^2-5x-2.25=0 equation: 


Simplifying
3x2 + -5x + -2.25 = 0

Reorder the terms:
-2.25 + -5x + 3x2 = 0

Solving
-2.25 + -5x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-0.75 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -1.666666667x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -1.666666667x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -1.666666667x + x2 = 0 + 0.75
-1.666666667x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-1.666666667x + x2 = 0.75

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 0.75 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 0.75 + 0.6944444447

Combine like terms: 0.75 + 0.6944444447 = 1.4444444447
0.6944444447 + -1.666666667x + x2 = 1.4444444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 1.4444444447

Calculate the square root of the right side: 1.201850425

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.201850425 and -1.201850425.


Subproblem 1
x + -0.8333333335 = 1.201850425

Simplifying
x + -0.8333333335 = 1.201850425

Reorder the terms:
-0.8333333335 + x = 1.201850425

Solving
-0.8333333335 + x = 1.201850425

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 1.201850425 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.201850425 + 0.8333333335
x = 1.201850425 + 0.8333333335

Combine like terms: 1.201850425 + 0.8333333335 = 2.0351837585
x = 2.0351837585

Simplifying
x = 2.0351837585


Subproblem 2
x + -0.8333333335 = -1.201850425

Simplifying
x + -0.8333333335 = -1.201850425

Reorder the terms:
-0.8333333335 + x = -1.201850425

Solving
-0.8333333335 + x = -1.201850425

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -1.201850425 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.201850425 + 0.8333333335
x = -1.201850425 + 0.8333333335

Combine like terms: -1.201850425 + 0.8333333335 = -0.3685170915
x = -0.3685170915

Simplifying
x = -0.3685170915


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0351837585, -0.3685170915}

See similar equations:

| -8(6n+4)=-320 | | -2x=10-18 | | (2x-5+x)2=38 | | 6(-6+5b)=-156 | | 12x=3x-45 | | x/6-7=-6 | | 7x=32-4 | | x(3x-2)-18x=5x(2-3x)+6 | | (x+6+9)2=52 | | r/18+6=5 | | 7x=35-14 | | 90+40= | | z^4-2iz^2+2i-1=0 | | 90=40 | | 2-3x-5=16-3 | | 3(2x+4)=-18 | | 3x+5-x=9 | | 3x+5-t=9 | | 198=l+2(w+2) | | -7b=98 | | 23-7x+21+5x=10 | | 198=x+2(x+2) | | 7y-(6y+3)=12 | | 2x+3=3x+12 | | 4-5=x | | x^2+0x+81= | | 4(2x+3)=9x-15-x | | 4a^2-9b^2=19 | | 3(y-5)=2(2y+1) | | 5x-3(x-3)=2(x+3) | | 2(3d-10)=40 | | 3p-(6-p)=18-2p |

Equations solver categories