55r^2-14r-23=0

Simple and best practice solution for 55r^2-14r-23=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 55r^2-14r-23=0 equation:


Simplifying
55r2 + -14r + -23 = 0

Reorder the terms:
-23 + -14r + 55r2 = 0

Solving
-23 + -14r + 55r2 = 0

Solving for variable 'r'.

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

Divide each side by '55'.
-0.4181818182 + -0.2545454545r + r2 = 0

Move the constant term to the right:

Add '0.4181818182' to each side of the equation.
-0.4181818182 + -0.2545454545r + 0.4181818182 + r2 = 0 + 0.4181818182

Reorder the terms:
-0.4181818182 + 0.4181818182 + -0.2545454545r + r2 = 0 + 0.4181818182

Combine like terms: -0.4181818182 + 0.4181818182 = 0.0000000000
0.0000000000 + -0.2545454545r + r2 = 0 + 0.4181818182
-0.2545454545r + r2 = 0 + 0.4181818182

Combine like terms: 0 + 0.4181818182 = 0.4181818182
-0.2545454545r + r2 = 0.4181818182

The r term is -0.2545454545r.  Take half its coefficient (-0.1272727273).
Square it (0.01619834711) and add it to both sides.

Add '0.01619834711' to each side of the equation.
-0.2545454545r + 0.01619834711 + r2 = 0.4181818182 + 0.01619834711

Reorder the terms:
0.01619834711 + -0.2545454545r + r2 = 0.4181818182 + 0.01619834711

Combine like terms: 0.4181818182 + 0.01619834711 = 0.43438016531
0.01619834711 + -0.2545454545r + r2 = 0.43438016531

Factor a perfect square on the left side:
(r + -0.1272727273)(r + -0.1272727273) = 0.43438016531

Calculate the square root of the right side: 0.659075235

Break this problem into two subproblems by setting 
(r + -0.1272727273) equal to 0.659075235 and -0.659075235.

Subproblem 1

r + -0.1272727273 = 0.659075235 Simplifying r + -0.1272727273 = 0.659075235 Reorder the terms: -0.1272727273 + r = 0.659075235 Solving -0.1272727273 + r = 0.659075235 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1272727273' to each side of the equation. -0.1272727273 + 0.1272727273 + r = 0.659075235 + 0.1272727273 Combine like terms: -0.1272727273 + 0.1272727273 = 0.0000000000 0.0000000000 + r = 0.659075235 + 0.1272727273 r = 0.659075235 + 0.1272727273 Combine like terms: 0.659075235 + 0.1272727273 = 0.7863479623 r = 0.7863479623 Simplifying r = 0.7863479623

Subproblem 2

r + -0.1272727273 = -0.659075235 Simplifying r + -0.1272727273 = -0.659075235 Reorder the terms: -0.1272727273 + r = -0.659075235 Solving -0.1272727273 + r = -0.659075235 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1272727273' to each side of the equation. -0.1272727273 + 0.1272727273 + r = -0.659075235 + 0.1272727273 Combine like terms: -0.1272727273 + 0.1272727273 = 0.0000000000 0.0000000000 + r = -0.659075235 + 0.1272727273 r = -0.659075235 + 0.1272727273 Combine like terms: -0.659075235 + 0.1272727273 = -0.5318025077 r = -0.5318025077 Simplifying r = -0.5318025077

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.7863479623, -0.5318025077}

See similar equations:

| 11+4x=7(x-1) | | 5z-9z=-7z-7-z | | 40=x(x+3) | | 2x+x/2+x+20=580 | | (5w+1)(2-w)=0 | | (1.5*b)*b=0 | | 1.5b*b=0 | | X*2=-9x-8 | | 3x-5-2x=5-12 | | 0.5(4x-2)= | | (5x-90)=2x+30 | | C-6c=0 | | (11r+6)(5r-4)=0 | | Y=0.6(100)+b | | 6n^2/2 | | x+13=5x | | 5(x)=5(2x-3) | | R=b^2+1 | | (5x)2=15x-45 | | 3c-1=c | | 3x-5-x=2x-3 | | 3ysquared= | | 3(2x+1)-2(3-2)=13 | | 15x-45/2=5x | | 1/3x3/8 | | (7a)x(2b)=0 | | 15/105 | | 9z+4-5z-5= | | -6(r-7)=-54 | | 8+9a=7 | | 4x+3+2y=11 | | 7x-4.23=0.2+2.57 |

Equations solver categories