x^2-1.5x=0.5

Simple and best practice solution for x^2-1.5x=0.5 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^2-1.5x=0.5 equation: 


Simplifying
x2 + -1.5x = 0.5

Reorder the terms:
-1.5x + x2 = 0.5

Solving
-1.5x + x2 = 0.5

Solving for variable 'x'.

Reorder the terms:
-0.5 + -1.5x + x2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + -1.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.5x + 0.5 + x2 = 0.0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.5x + x2 = 0.0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.5x + x2 = 0.0 + 0.5
-1.5x + x2 = 0.0 + 0.5

Combine like terms: 0.0 + 0.5 = 0.5
-1.5x + x2 = 0.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 0.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 0.5 + 0.5625

Combine like terms: 0.5 + 0.5625 = 1.0625
0.5625 + -1.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.030776406 and -1.030776406.


Subproblem 1
x + -0.75 = 1.030776406

Simplifying
x + -0.75 = 1.030776406

Reorder the terms:
-0.75 + x = 1.030776406

Solving
-0.75 + x = 1.030776406

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.030776406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.030776406 + 0.75
x = 1.030776406 + 0.75

Combine like terms: 1.030776406 + 0.75 = 1.780776406
x = 1.780776406

Simplifying
x = 1.780776406


Subproblem 2
x + -0.75 = -1.030776406

Simplifying
x + -0.75 = -1.030776406

Reorder the terms:
-0.75 + x = -1.030776406

Solving
-0.75 + x = -1.030776406

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.030776406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.030776406 + 0.75
x = -1.030776406 + 0.75

Combine like terms: -1.030776406 + 0.75 = -0.280776406
x = -0.280776406

Simplifying
x = -0.280776406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.780776406, -0.280776406}

See similar equations:

| x-1.5x=0.5 | | x-1.5=0.5 | | x+6=37 | | r^2+4r-45=0 | | 4m^2-3m=0 | | 10(x+2)=6(x+2) | | 3z+9= | | x+5=37 | | 24=4x+2(x+3) | | 0=(r+4)(4r-8) | | x^2-2x=37 | | 2(x+3)+6=20 | | x-0.15x+10=180 | | (2w-3)(w+12)=0 | | 2(x+1)=4(7x+2) | | 6(4x-5)=2(12x+3) | | (2m-9)m=0 | | 2(x+1)=4(2x+2) | | 3m+9+2m=m-2m-3 | | 5-3r*2=-7 | | x-0.15x+10=116.25 | | 21+m=32 | | 3x^2-31x=-6x^2-5x-16 | | 0=(2h-5)h | | 5y+4+-3= | | 4x^2-20x=1 | | -18=9(a+1) | | 20r^2-11r-3=0 | | 8+5s-2=9s+27-7s | | 2y=-6x-3 | | 6(x+5)=18 | | 10x^2+56= |

Equations solver categories