r^2-7r+3=0

Simple and best practice solution for r^2-7r+3=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^2-7r+3=0 equation:


Simplifying
r2 + -7r + 3 = 0

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

Solving
3 + -7r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The r term is -7r.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7r + 12.25 + r2 = -3 + 12.25

Reorder the terms:
12.25 + -7r + r2 = -3 + 12.25

Combine like terms: -3 + 12.25 = 9.25
12.25 + -7r + r2 = 9.25

Factor a perfect square on the left side:
(r + -3.5)(r + -3.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(r + -3.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

r + -3.5 = 3.041381265 Simplifying r + -3.5 = 3.041381265 Reorder the terms: -3.5 + r = 3.041381265 Solving -3.5 + r = 3.041381265 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = 3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 3.041381265 + 3.5 r = 3.041381265 + 3.5 Combine like terms: 3.041381265 + 3.5 = 6.541381265 r = 6.541381265 Simplifying r = 6.541381265

Subproblem 2

r + -3.5 = -3.041381265 Simplifying r + -3.5 = -3.041381265 Reorder the terms: -3.5 + r = -3.041381265 Solving -3.5 + r = -3.041381265 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = -3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -3.041381265 + 3.5 r = -3.041381265 + 3.5 Combine like terms: -3.041381265 + 3.5 = 0.458618735 r = 0.458618735 Simplifying r = 0.458618735

Solution

The solution to the problem is based on the solutions from the subproblems. r = {6.541381265, 0.458618735}

See similar equations:

| -5+(4-2x)-8x+5= | | 9z^2+24z+16= | | 3x-5=x+(5+x) | | (3x+1)-(-3x-7)-9x= | | -(6x-6)+(4x-8)= | | -9+x+3(-8+5x)= | | 2x+10+4x+1=29 | | 4.8x^2-x-4=0 | | 4.8x-4-x=0 | | 12x-16=8+4 | | 6+6x-(2x+8)-(2x+4)= | | (2x-6)-(-9x-1)= | | 8+3s-(5s+7)-(5s+8)= | | x^3-2x^2-x-2=0 | | 18x+8=12x+3 | | 4.8x^2-4-x=0 | | A=2x^2+2y^2+2xy-4x-6y | | 12x^3-18x^2=0 | | 6x^2(2x-3)=0 | | 6(2k+3)-5k= | | 4x-8+4x=6(2-2x) | | -8x-(-2x+4)= | | 14x-28=20 | | 3x=-8+2 | | 3x=20-8 | | 2x=30-6 | | 8-3x-3=x-4+2x | | x+4=4x+1 | | y=-0.04x^2+0.6x+2 | | n+31=50 | | n+13=21 | | 4x=30+2 |

Equations solver categories