r^2+3r=7

Simple and best practice solution for r^2+3r=7 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+3r=7 equation: 


Simplifying
r2 + 3r = 7

Reorder the terms:
3r + r2 = 7

Solving
3r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + 3r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 3r + 7 + r2 = 0 + 7

Reorder the terms:
-7 + 7 + 3r + r2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3r + r2 = 0 + 7
3r + r2 = 0 + 7

Combine like terms: 0 + 7 = 7
3r + r2 = 7

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 7 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + 3r + r2 = 9.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(r + 1.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
r + 1.5 = 3.041381265

Simplifying
r + 1.5 = 3.041381265

Reorder the terms:
1.5 + r = 3.041381265

Solving
1.5 + r = 3.041381265

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 3.041381265 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 3.041381265 + -1.5
r = 3.041381265 + -1.5

Combine like terms: 3.041381265 + -1.5 = 1.541381265
r = 1.541381265

Simplifying
r = 1.541381265


Subproblem 2
r + 1.5 = -3.041381265

Simplifying
r + 1.5 = -3.041381265

Reorder the terms:
1.5 + r = -3.041381265

Solving
1.5 + r = -3.041381265

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -3.041381265 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -3.041381265 + -1.5
r = -3.041381265 + -1.5

Combine like terms: -3.041381265 + -1.5 = -4.541381265
r = -4.541381265

Simplifying
r = -4.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.541381265, -4.541381265}

See similar equations:

| 3x^3-5x^2-12x=0 | | x+40+25=180 | | x+(4x+10)+2(4x+10)=1280 | | 58+47+x=180 | | -8v^2-34v-15=0 | | 10-(2x-5)=x | | log(3)=log(5)+log(x-4) | | (2x+5)-(x-6)(x)= | | 30x+700=4300 | | (2x-5)+(x+6)(x)= | | 7m-8=69 | | 5(15x+100)=1100 | | 2(x-3)-4(x+5)=7x+1 | | (2x-5)(x+6)(X)= | | (2x-5)(x+6)x= | | 7-x^2=0 | | (2x-5)(x+6)= | | 0.12x=.60 | | 10+2a=10+2a | | (2x-5)(x+6)(2)= | | 4x+14y-8=6 | | (2x-5)-(x+6)= | | 5.5+1x=105 | | 18=10b+5 | | 1.06(1.22)(5-x)=6 | | -3(10-1)= | | 5.5+1x=54.5 | | x-3+11=-1 | | 0.16x(x-18)+.50(x+2)=x-20 | | x-2(-3x+8)=-2 | | 2b+24=16b+7 | | 145x+3325=6089.50 |

Equations solver categories