r^2+2r-54=0

Simple and best practice solution for r^2+2r-54=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 r^2+2r-54=0 equation:


Simplifying
r2 + 2r + -54 = 0

Reorder the terms:
-54 + 2r + r2 = 0

Solving
-54 + 2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 2r + 54 + r2 = 0 + 54

Reorder the terms:
-54 + 54 + 2r + r2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 2r + r2 = 0 + 54
2r + r2 = 0 + 54

Combine like terms: 0 + 54 = 54
2r + r2 = 54

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 54 + 1

Reorder the terms:
1 + 2r + r2 = 54 + 1

Combine like terms: 54 + 1 = 55
1 + 2r + r2 = 55

Factor a perfect square on the left side:
(r + 1)(r + 1) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(r + 1) equal to 7.416198487 and -7.416198487.

Subproblem 1

r + 1 = 7.416198487 Simplifying r + 1 = 7.416198487 Reorder the terms: 1 + r = 7.416198487 Solving 1 + r = 7.416198487 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + r = 7.416198487 + -1 r = 7.416198487 + -1 Combine like terms: 7.416198487 + -1 = 6.416198487 r = 6.416198487 Simplifying r = 6.416198487

Subproblem 2

r + 1 = -7.416198487 Simplifying r + 1 = -7.416198487 Reorder the terms: 1 + r = -7.416198487 Solving 1 + r = -7.416198487 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + r = -7.416198487 + -1 r = -7.416198487 + -1 Combine like terms: -7.416198487 + -1 = -8.416198487 r = -8.416198487 Simplifying r = -8.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. r = {6.416198487, -8.416198487}

See similar equations:

| 96/1024 | | x+(-19+17)=63 | | 6e^2x=78 | | 3-6/5 | | (x+1)(x+4)=(2-x)(x+2) | | 121q^2-9=0 | | f/6=22.5 | | 5u^2-53=-53 | | y=e^4*lnx | | v^2=94 | | 2(x-3)+5x(x-1)=5x^2 | | q^2=83 | | 3g^2=75 | | 2x-3y=-6fory | | 1.6y-4=2 | | 8x*5x=12.666 | | 5sin(3x+1)=0 | | 2(2x+3)=6(x-2)+10 | | x(1+1.1x+1.4x^2)=0.2 | | 12ab-c-6ca+2b=0 | | 12ab+-1c+-6ca+2b=0 | | 12ab+-6ac+2b+-1c= | | (2/9)-5x=6 | | 6-4(4x+3)=2(x-1) | | 3x+8=4x+12 | | b*5=15 | | x+5=5x+21 | | 3x-(10x+7)-2[2x-3(4x+3)+1]+3=8x+3 | | 4-(3+5x)=7x-2(8-3x) | | 6x=3(x+4)+3 | | D-2(4+d)=4 | | 40=5(x-3)+3 |

Equations solver categories