5r^2+24r+5=0

Simple and best practice solution for 5r^2+24r+5=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 5r^2+24r+5=0 equation:


Simplifying
5r2 + 24r + 5 = 0

Reorder the terms:
5 + 24r + 5r2 = 0

Solving
5 + 24r + 5r2 = 0

Solving for variable 'r'.

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

Divide each side by '5'.
1 + 4.8r + r2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4.8r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + 4.8r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4.8r + r2 = 0 + -1
4.8r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
4.8r + r2 = -1

The r term is 4.8r.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8r + 5.76 + r2 = -1 + 5.76

Reorder the terms:
5.76 + 4.8r + r2 = -1 + 5.76

Combine like terms: -1 + 5.76 = 4.76
5.76 + 4.8r + r2 = 4.76

Factor a perfect square on the left side:
(r + 2.4)(r + 2.4) = 4.76

Calculate the square root of the right side: 2.181742423

Break this problem into two subproblems by setting 
(r + 2.4) equal to 2.181742423 and -2.181742423.

Subproblem 1

r + 2.4 = 2.181742423 Simplifying r + 2.4 = 2.181742423 Reorder the terms: 2.4 + r = 2.181742423 Solving 2.4 + r = 2.181742423 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + r = 2.181742423 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = 2.181742423 + -2.4 r = 2.181742423 + -2.4 Combine like terms: 2.181742423 + -2.4 = -0.218257577 r = -0.218257577 Simplifying r = -0.218257577

Subproblem 2

r + 2.4 = -2.181742423 Simplifying r + 2.4 = -2.181742423 Reorder the terms: 2.4 + r = -2.181742423 Solving 2.4 + r = -2.181742423 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + r = -2.181742423 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = -2.181742423 + -2.4 r = -2.181742423 + -2.4 Combine like terms: -2.181742423 + -2.4 = -4.581742423 r = -4.581742423 Simplifying r = -4.581742423

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.218257577, -4.581742423}

See similar equations:

| -10=4v+6 | | 36=2y+2(y+6) | | -3b+8-5d=18 | | 22(3x-6)= | | 32=9(5b-7) | | 8m^2+10m+5=0 | | 3p-2=54 | | 9x-5x+2x=33-13+22 | | 8(1-3k)=-26 | | 2x-25=5x+17 | | 2(x+1)=3(x-3) | | 22=6v+7(v-8) | | 5(8h-6)=20 | | -6+6p=9(5p-18) | | 5x+8-7(x+1)=6x+4 | | 57=7+5x | | -14=5u+2(u+7) | | 4(X-3)=2x+13 | | 2+6r=11-3r | | -8=2-5v | | 22x^8y^2+11xy= | | -2+3(1-8f)=21 | | 621.72=6.28r^2+6.28r(18.1) | | 17+11b=-5(-4b+20) | | 16y= | | 14=-2(u+1) | | 3(2(0.3)-5)+31=14 | | 5g-10-12=15g+8(-2g+10) | | 4(5x+2)=10(2x+1) | | 10x-41=6x-5 | | 3x-2(5-4(2x-(1-x)))=36 | | 41=4v+1 |

Equations solver categories