7r^2-7r-12=0

Simple and best practice solution for 7r^2-7r-12=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 7r^2-7r-12=0 equation:


Simplifying
7r2 + -7r + -12 = 0

Reorder the terms:
-12 + -7r + 7r2 = 0

Solving
-12 + -7r + 7r2 = 0

Solving for variable 'r'.

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

Divide each side by '7'.
-1.714285714 + -1r + r2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + -1r + 1.714285714 + r2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + -1r + r2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + -1r + r2 = 0 + 1.714285714
-1r + r2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
-1r + r2 = 1.714285714

The r term is -1r.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1r + 0.25 + r2 = 1.714285714 + 0.25

Reorder the terms:
0.25 + -1r + r2 = 1.714285714 + 0.25

Combine like terms: 1.714285714 + 0.25 = 1.964285714
0.25 + -1r + r2 = 1.964285714

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = 1.964285714

Calculate the square root of the right side: 1.401529776

Break this problem into two subproblems by setting 
(r + -0.5) equal to 1.401529776 and -1.401529776.

Subproblem 1

r + -0.5 = 1.401529776 Simplifying r + -0.5 = 1.401529776 Reorder the terms: -0.5 + r = 1.401529776 Solving -0.5 + r = 1.401529776 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 1.401529776 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 1.401529776 + 0.5 r = 1.401529776 + 0.5 Combine like terms: 1.401529776 + 0.5 = 1.901529776 r = 1.901529776 Simplifying r = 1.901529776

Subproblem 2

r + -0.5 = -1.401529776 Simplifying r + -0.5 = -1.401529776 Reorder the terms: -0.5 + r = -1.401529776 Solving -0.5 + r = -1.401529776 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -1.401529776 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -1.401529776 + 0.5 r = -1.401529776 + 0.5 Combine like terms: -1.401529776 + 0.5 = -0.901529776 r = -0.901529776 Simplifying r = -0.901529776

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.901529776, -0.901529776}

See similar equations:

| -12x-4=-44 | | y+2x-2=5 | | 8*2/3n=7/8 | | 0.5(y+9)=2(y-6) | | .83=x^4 | | 9x-4/3 | | 4=3+3x | | 17(x-5)=6-5+7 | | 17(x-5)=6(7-x) | | 5x/11(8-7)=-1 | | 17(x-5)=6(7-x)-7x | | e=m+c*c | | 18n+.5=6(3n+25) | | 5x+14=-40-4x | | 4w+8y+8x+6x-13y+3w= | | -3x-21=6 | | 4X^2+x-30=3-2x(5-2x) | | -10y=9x-17 | | 5x^2=15xy^2 | | 5ln(2x+8)=22 | | 10a-18b=0 | | 9-13=-4 | | y-4=1.9(x-2) | | -11y+6y= | | -6(6n-5)+3n=-102 | | -2x/7-6-9 | | 5w^2-1=2w | | 1.54g-6=0.93 | | x^3+2x^2-9x-18= | | 7x-(8)=13 | | 5x+4=9x-4 | | f(x)=10+7 |

Equations solver categories