6r^2-10=r

Simple and best practice solution for 6r^2-10=r 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 6r^2-10=r equation:


Simplifying
6r2 + -10 = r

Reorder the terms:
-10 + 6r2 = r

Solving
-10 + 6r2 = r

Solving for variable 'r'.

Reorder the terms:
-10 + -1r + 6r2 = r + -1r

Combine like terms: r + -1r = 0
-10 + -1r + 6r2 = 0

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

Divide each side by '6'.
-1.666666667 + -0.1666666667r + r2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -0.1666666667r + 1.666666667 + r2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -0.1666666667r + r2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -0.1666666667r + r2 = 0 + 1.666666667
-0.1666666667r + r2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-0.1666666667r + r2 = 1.666666667

The r term is -0.1666666667r.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667r + 0.006944444447 + r2 = 1.666666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667r + r2 = 1.666666667 + 0.006944444447

Combine like terms: 1.666666667 + 0.006944444447 = 1.673611111447
0.006944444447 + -0.1666666667r + r2 = 1.673611111447

Factor a perfect square on the left side:
(r + -0.08333333335)(r + -0.08333333335) = 1.673611111447

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(r + -0.08333333335) equal to 1.293681225 and -1.293681225.

Subproblem 1

r + -0.08333333335 = 1.293681225 Simplifying r + -0.08333333335 = 1.293681225 Reorder the terms: -0.08333333335 + r = 1.293681225 Solving -0.08333333335 + r = 1.293681225 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + r = 1.293681225 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + r = 1.293681225 + 0.08333333335 r = 1.293681225 + 0.08333333335 Combine like terms: 1.293681225 + 0.08333333335 = 1.37701455835 r = 1.37701455835 Simplifying r = 1.37701455835

Subproblem 2

r + -0.08333333335 = -1.293681225 Simplifying r + -0.08333333335 = -1.293681225 Reorder the terms: -0.08333333335 + r = -1.293681225 Solving -0.08333333335 + r = -1.293681225 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + r = -1.293681225 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + r = -1.293681225 + 0.08333333335 r = -1.293681225 + 0.08333333335 Combine like terms: -1.293681225 + 0.08333333335 = -1.21034789165 r = -1.21034789165 Simplifying r = -1.21034789165

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.37701455835, -1.21034789165}

See similar equations:

| 0.7(x+7)+1.7(x-6)= | | -4x^3+2x-6=0 | | 27+-6=3 | | 4y+6w=2 | | 5(x-4)=3(x+1.5) | | 3x-4y+7a= | | 5.0m+6.25+3.1m= | | (-2x)(-3y)(-z)= | | m=2,(-2,-3) | | -1.6(x-3.7)=1.375 | | 0=160t-1000 | | 14x^2+4-5x+x-2x^2+8= | | s(t)=8t^2+32t | | 16x^2+2+2x-15x^2-1+14x= | | 2m-3(9m+1)=7m+4(7+5m) | | b^2+19b-1100=0 | | a^2+14a+-51=0 | | 6r+8r=13 | | 8x+30=2x+126 | | 11a+3s=6848 | | 6t^2=56 | | a+s=1008 | | 4p-15=-39+8p | | 11a+3s=1008 | | 7m-7=-27+2 | | y=2x^3-12x^2-72x+18 | | 385+X=100 | | 36+12x-12=-6 | | 10=6x+b | | 3y^2-9y-12=0 | | 3(x^2-7)=9 | | b^2-82b+1677=0 |

Equations solver categories