0=4r^2-21r+24

Simple and best practice solution for 0=4r^2-21r+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=4r^2-21r+24 equation:


Simplifying
0 = 4r2 + -21r + 24

Reorder the terms:
0 = 24 + -21r + 4r2

Solving
0 = 24 + -21r + 4r2

Solving for variable 'r'.

Combine like terms: 0 + -24 = -24
-24 + 21r + -4r2 = 24 + -21r + 4r2 + -24 + 21r + -4r2

Reorder the terms:
-24 + 21r + -4r2 = 24 + -24 + -21r + 21r + 4r2 + -4r2

Combine like terms: 24 + -24 = 0
-24 + 21r + -4r2 = 0 + -21r + 21r + 4r2 + -4r2
-24 + 21r + -4r2 = -21r + 21r + 4r2 + -4r2

Combine like terms: -21r + 21r = 0
-24 + 21r + -4r2 = 0 + 4r2 + -4r2
-24 + 21r + -4r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
-24 + 21r + -4r2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
6 + -5.25r + r2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -5.25r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + -5.25r + r2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5.25r + r2 = 0 + -6
-5.25r + r2 = 0 + -6

Combine like terms: 0 + -6 = -6
-5.25r + r2 = -6

The r term is -5.25r.  Take half its coefficient (-2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
-5.25r + 6.890625 + r2 = -6 + 6.890625

Reorder the terms:
6.890625 + -5.25r + r2 = -6 + 6.890625

Combine like terms: -6 + 6.890625 = 0.890625
6.890625 + -5.25r + r2 = 0.890625

Factor a perfect square on the left side:
(r + -2.625)(r + -2.625) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(r + -2.625) equal to 0.943729304 and -0.943729304.

Subproblem 1

r + -2.625 = 0.943729304 Simplifying r + -2.625 = 0.943729304 Reorder the terms: -2.625 + r = 0.943729304 Solving -2.625 + r = 0.943729304 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + r = 0.943729304 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + r = 0.943729304 + 2.625 r = 0.943729304 + 2.625 Combine like terms: 0.943729304 + 2.625 = 3.568729304 r = 3.568729304 Simplifying r = 3.568729304

Subproblem 2

r + -2.625 = -0.943729304 Simplifying r + -2.625 = -0.943729304 Reorder the terms: -2.625 + r = -0.943729304 Solving -2.625 + r = -0.943729304 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + r = -0.943729304 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + r = -0.943729304 + 2.625 r = -0.943729304 + 2.625 Combine like terms: -0.943729304 + 2.625 = 1.681270696 r = 1.681270696 Simplifying r = 1.681270696

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.568729304, 1.681270696}

See similar equations:

| 8p-3=9p+4 | | 2(2x+12)=68 | | 12+(-9)=5+p | | 1/4(3/11-4x)-9/11=3/11 | | (Z+13)+(z+10)+z=360 | | 3(t+2)-2t=2 | | Xy-3x=4 | | -5-5(x+4)+4x=9-5 | | 4x^3-20x^2-11x=0 | | 102=40x-18 | | 3u+9=-4 | | 8y-16=10y-9+6 | | b+(-6)=-20 | | 3u+9=4 | | -5-7x+8x=4-5 | | -1g+14=-12 | | 2/3x-2=4/6 | | 6x-18x+36=2(y+3) | | 40=9+k | | 10x=10x-2 | | d^4/6=18 | | Pfk-l=m | | X+(-28)=0 | | 4=-7a+9a | | 75=19+n | | -7g+9=-12 | | 6.3=1.2x-0.9 | | (2x+12)=(6x-18) | | -5x-2=-1+2x | | 1.333b+.5=2.5 | | 12x^3-5x^2-7x=0 | | 0.8(z+3)=0.7(z+4) |

Equations solver categories