12x^2-47x+18=0

Simple and best practice solution for 12x^2-47x+18=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 12x^2-47x+18=0 equation:


Simplifying
12x2 + -47x + 18 = 0

Reorder the terms:
18 + -47x + 12x2 = 0

Solving
18 + -47x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
1.5 + -3.916666667x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -3.916666667x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -3.916666667x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3.916666667x + x2 = 0 + -1.5
-3.916666667x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-3.916666667x + x2 = -1.5

The x term is -3.916666667x.  Take half its coefficient (-1.958333334).
Square it (3.835069447) and add it to both sides.

Add '3.835069447' to each side of the equation.
-3.916666667x + 3.835069447 + x2 = -1.5 + 3.835069447

Reorder the terms:
3.835069447 + -3.916666667x + x2 = -1.5 + 3.835069447

Combine like terms: -1.5 + 3.835069447 = 2.335069447
3.835069447 + -3.916666667x + x2 = 2.335069447

Factor a perfect square on the left side:
(x + -1.958333334)(x + -1.958333334) = 2.335069447

Calculate the square root of the right side: 1.528093403

Break this problem into two subproblems by setting 
(x + -1.958333334) equal to 1.528093403 and -1.528093403.

Subproblem 1

x + -1.958333334 = 1.528093403 Simplifying x + -1.958333334 = 1.528093403 Reorder the terms: -1.958333334 + x = 1.528093403 Solving -1.958333334 + x = 1.528093403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.958333334' to each side of the equation. -1.958333334 + 1.958333334 + x = 1.528093403 + 1.958333334 Combine like terms: -1.958333334 + 1.958333334 = 0.000000000 0.000000000 + x = 1.528093403 + 1.958333334 x = 1.528093403 + 1.958333334 Combine like terms: 1.528093403 + 1.958333334 = 3.486426737 x = 3.486426737 Simplifying x = 3.486426737

Subproblem 2

x + -1.958333334 = -1.528093403 Simplifying x + -1.958333334 = -1.528093403 Reorder the terms: -1.958333334 + x = -1.528093403 Solving -1.958333334 + x = -1.528093403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.958333334' to each side of the equation. -1.958333334 + 1.958333334 + x = -1.528093403 + 1.958333334 Combine like terms: -1.958333334 + 1.958333334 = 0.000000000 0.000000000 + x = -1.528093403 + 1.958333334 x = -1.528093403 + 1.958333334 Combine like terms: -1.528093403 + 1.958333334 = 0.430239931 x = 0.430239931 Simplifying x = 0.430239931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.486426737, 0.430239931}

See similar equations:

| 3x+18=12-24 | | 3(w-4)-6w=-3 | | x^4+8x^3-x^2+2=0 | | z+6=9*3 | | n-(-16)=28 | | 0.1v-0.003+0.3v=0.17 | | 3x^2+2x-3=9 | | 1.2r=9.5 | | 10x+5y=15x+4y | | 2(2a+c)=22 | | (3x+12)-(5x-6)=0 | | 4w+10(21.2+-0.4w)=212 | | -13=n-(-13) | | (x+4)-2(4-3x)=4(x+3)-1 | | 5p-17=2(2p-11) | | 6x-4x+x-8+6-4=0 | | 5*log(x)=12 | | -37=r-12 | | 5log(x)=12 | | 6x-4+x-8+6-4=0 | | 4x-(x+1)=-4+5(x-5) | | 4w+10c=212 | | 1.2x+14.8=3.3x-2 | | 9x+49=1199 | | -x-88=7x+104 | | 88=P(88+54+49) | | 3(a+4)=30 | | -5x+3=-3-2x | | 0.9(x+4)+1.9(x-3)= | | -50-7x=-10x+28 | | x+87+125+63+169=540 | | 7x+4=10+6x |

Equations solver categories