0=x^2-21x+24

Simple and best practice solution for 0=x^2-21x+24 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=x^2-21x+24 equation:


Simplifying
0 = x2 + -21x + 24

Reorder the terms:
0 = 24 + -21x + x2

Solving
0 = 24 + -21x + x2

Solving for variable 'x'.

Combine like terms: 0 + -24 = -24
-24 + 21x + -1x2 = 24 + -21x + x2 + -24 + 21x + -1x2

Reorder the terms:
-24 + 21x + -1x2 = 24 + -24 + -21x + 21x + x2 + -1x2

Combine like terms: 24 + -24 = 0
-24 + 21x + -1x2 = 0 + -21x + 21x + x2 + -1x2
-24 + 21x + -1x2 = -21x + 21x + x2 + -1x2

Combine like terms: -21x + 21x = 0
-24 + 21x + -1x2 = 0 + x2 + -1x2
-24 + 21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + 21x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
24 + -21x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -21x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -21x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -21x + x2 = 0 + -24
-21x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-21x + x2 = -24

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -24 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -24 + 110.25

Combine like terms: -24 + 110.25 = 86.25
110.25 + -21x + x2 = 86.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 86.25

Calculate the square root of the right side: 9.287087811

Break this problem into two subproblems by setting 
(x + -10.5) equal to 9.287087811 and -9.287087811.

Subproblem 1

x + -10.5 = 9.287087811 Simplifying x + -10.5 = 9.287087811 Reorder the terms: -10.5 + x = 9.287087811 Solving -10.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 9.287087811 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.287087811 + 10.5 x = 9.287087811 + 10.5 Combine like terms: 9.287087811 + 10.5 = 19.787087811 x = 19.787087811 Simplifying x = 19.787087811

Subproblem 2

x + -10.5 = -9.287087811 Simplifying x + -10.5 = -9.287087811 Reorder the terms: -10.5 + x = -9.287087811 Solving -10.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -9.287087811 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.287087811 + 10.5 x = -9.287087811 + 10.5 Combine like terms: -9.287087811 + 10.5 = 1.212912189 x = 1.212912189 Simplifying x = 1.212912189

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.787087811, 1.212912189}

See similar equations:

| 8-0.5(x+3)=0.25(x+-1) | | -(4-m)=10 | | 6=-4k+2 | | 20y+2=46 | | 1.33*4=y | | s*7-17=137 | | x^2+x+m-1=0 | | 5(x+3)-3=2(x+8) | | 43-4=y | | 9h-16=74 | | 9m-15=58 | | 5n^2+7n=-2 | | 8x+12y-20= | | 40+16x= | | 3(25-10h+h^2)-20+4h-(75-20)= | | 15x-28= | | 0=x^2-16x-225 | | 6x+27= | | x^7=65 | | 4.9x^2-20x=0 | | 8+(y+2)=4(y-3) | | x+(x*0.25)=500000 | | 3n+4-4=n+20 | | 4t^2-9s^2=0 | | lnx^2-6lnx+5=0 | | (5x-2)-(3x-1)=(4x+3)-(5x-2) | | 7(-1+h)-5(-1)= | | 2lnx+ln(2x-3)=ln(3x-2) | | 0.63=logx | | 3(-5+h)-4(-5)= | | 3(25-2h+h^2)-4+4h-(4-3)= | | 9b^2+42bg+49g^2= |

Equations solver categories