5r^2+24r-1=0

Simple and best practice solution for 5r^2+24r-1=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-1=0 equation:


Simplifying
5r2 + 24r + -1 = 0

Reorder the terms:
-1 + 24r + 5r2 = 0

Solving
-1 + 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'.
-0.2 + 4.8r + r2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 4.8r + 0.2 + r2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 4.8r + r2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 4.8r + r2 = 0 + 0.2
4.8r + r2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
4.8r + r2 = 0.2

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 = 0.2 + 5.76

Reorder the terms:
5.76 + 4.8r + r2 = 0.2 + 5.76

Combine like terms: 0.2 + 5.76 = 5.96
5.76 + 4.8r + r2 = 5.96

Factor a perfect square on the left side:
(r + 2.4)(r + 2.4) = 5.96

Calculate the square root of the right side: 2.441311123

Break this problem into two subproblems by setting 
(r + 2.4) equal to 2.441311123 and -2.441311123.

Subproblem 1

r + 2.4 = 2.441311123 Simplifying r + 2.4 = 2.441311123 Reorder the terms: 2.4 + r = 2.441311123 Solving 2.4 + r = 2.441311123 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 = 2.441311123 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = 2.441311123 + -2.4 r = 2.441311123 + -2.4 Combine like terms: 2.441311123 + -2.4 = 0.041311123 r = 0.041311123 Simplifying r = 0.041311123

Subproblem 2

r + 2.4 = -2.441311123 Simplifying r + 2.4 = -2.441311123 Reorder the terms: 2.4 + r = -2.441311123 Solving 2.4 + r = -2.441311123 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 = -2.441311123 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + r = -2.441311123 + -2.4 r = -2.441311123 + -2.4 Combine like terms: -2.441311123 + -2.4 = -4.841311123 r = -4.841311123 Simplifying r = -4.841311123

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.041311123, -4.841311123}

See similar equations:

| 5(7+w)=4(2+w) | | 2-3x=4-5x | | q=300-6(0) | | 10x-6+3x-3=9x-3+3x | | 15a-25=-13 | | 8x-3=7x+5 | | -11=9+p | | 4x^2+25x+25=-6x+4 | | -9+5x=1 | | -9(z+3)+5(3z-3)=5(z-4)+14 | | 2x^2-8x-11=0 | | 5(n-6)-(2-3n)=7n | | (3+7y)-(6-5y)= | | 3.063296521985267968968595445768796909606+453736356375-1.7356738264= | | 4x+1-x=5+2x+5 | | -0.00004826099263+-0.00004826099263-0.7658(4)= | | 6z-8=7z-7 | | 12+34+56+46+24+45+34+23+5677463a= | | y-5.3=2 | | x+3x*2=120 | | 2x+2(x-6)=72 | | 0.36+0.26=3.86 | | B=pt+p | | 0=(1/4)p | | 8-(6x+5)=11 | | 2+3=25 | | 2+3=23 | | 8+2m-2=8m+12-5m | | a+(2a+7)+(2b+2)=366 | | n^2+9n-162=0 | | 2x(x+5)=0 | | (5x-7)(3x+3)=12((x+1)(x+1))-3x(9-x) |

Equations solver categories