0.5*x^2-3x=27

Simple and best practice solution for 0.5*x^2-3x=27 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 0.5*x^2-3x=27 equation:


Simplifying
0.5x2 + -3x = 27

Reorder the terms:
-3x + 0.5x2 = 27

Solving
-3x + 0.5x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + -3x + 0.5x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -3x + 0.5x2 = 0

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

Divide each side by '0.5'.
-54 + -6x + x2 = 0

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -6x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -6x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -6x + x2 = 0 + 54
-6x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-6x + x2 = 54

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 54 + 9

Reorder the terms:
9 + -6x + x2 = 54 + 9

Combine like terms: 54 + 9 = 63
9 + -6x + x2 = 63

Factor a perfect square on the left side:
(x + -3)(x + -3) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + -3) equal to 7.937253933 and -7.937253933.

Subproblem 1

x + -3 = 7.937253933 Simplifying x + -3 = 7.937253933 Reorder the terms: -3 + x = 7.937253933 Solving -3 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 7.937253933 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.937253933 + 3 x = 7.937253933 + 3 Combine like terms: 7.937253933 + 3 = 10.937253933 x = 10.937253933 Simplifying x = 10.937253933

Subproblem 2

x + -3 = -7.937253933 Simplifying x + -3 = -7.937253933 Reorder the terms: -3 + x = -7.937253933 Solving -3 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -7.937253933 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.937253933 + 3 x = -7.937253933 + 3 Combine like terms: -7.937253933 + 3 = -4.937253933 x = -4.937253933 Simplifying x = -4.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.937253933, -4.937253933}

See similar equations:

| 2y-5=y+10 | | -3x-(-1)=4 | | 5x+1x+14x-46=180 | | w+9=996 | | v-9.5=3.78 | | -3(0)-y=4 | | -3(0)-y=6 | | (9-0)=12 | | -9f=-270 | | -0.5s^2t^5-0.5s^2t^5=0 | | m^2=48+2m | | z+51=480 | | 4x+112+56=180 | | 5x+31=8x-8 | | 5x+1y=6 | | (x+10)+(x-2)= | | 1x+2=4x+7 | | 7x-5=3+15 | | 8q-6+9q= | | -5(v+8)=3v-28 | | -3x-(-13)=4 | | 14x+2=4x+3 | | 5j=55 | | -6(2x-2)+7=-12x+19 | | u+39=82 | | 5x-2+90+2x+8=180 | | x=e(In5/In2) | | 2x+2=4x+11 | | 7(x+3)-6=22-3x-7+10x | | 2x^3-3x^2-4x+12=0 | | 5x-2+90+2x+8=80 | | 6(x+1)=4x-1 |

Equations solver categories