7r^2+14r-40=7

Simple and best practice solution for 7r^2+14r-40=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 7r^2+14r-40=7 equation:


Simplifying
7r2 + 14r + -40 = 7

Reorder the terms:
-40 + 14r + 7r2 = 7

Solving
-40 + 14r + 7r2 = 7

Solving for variable 'r'.

Reorder the terms:
-40 + -7 + 14r + 7r2 = 7 + -7

Combine like terms: -40 + -7 = -47
-47 + 14r + 7r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-47 + 14r + 7r2 = 0

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

Divide each side by '7'.
-6.714285714 + 2r + r2 = 0

Move the constant term to the right:

Add '6.714285714' to each side of the equation.
-6.714285714 + 2r + 6.714285714 + r2 = 0 + 6.714285714

Reorder the terms:
-6.714285714 + 6.714285714 + 2r + r2 = 0 + 6.714285714

Combine like terms: -6.714285714 + 6.714285714 = 0.000000000
0.000000000 + 2r + r2 = 0 + 6.714285714
2r + r2 = 0 + 6.714285714

Combine like terms: 0 + 6.714285714 = 6.714285714
2r + r2 = 6.714285714

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 = 6.714285714 + 1

Reorder the terms:
1 + 2r + r2 = 6.714285714 + 1

Combine like terms: 6.714285714 + 1 = 7.714285714
1 + 2r + r2 = 7.714285714

Factor a perfect square on the left side:
(r + 1)(r + 1) = 7.714285714

Calculate the square root of the right side: 2.777460299

Break this problem into two subproblems by setting 
(r + 1) equal to 2.777460299 and -2.777460299.

Subproblem 1

r + 1 = 2.777460299 Simplifying r + 1 = 2.777460299 Reorder the terms: 1 + r = 2.777460299 Solving 1 + r = 2.777460299 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 = 2.777460299 + -1 Combine like terms: 1 + -1 = 0 0 + r = 2.777460299 + -1 r = 2.777460299 + -1 Combine like terms: 2.777460299 + -1 = 1.777460299 r = 1.777460299 Simplifying r = 1.777460299

Subproblem 2

r + 1 = -2.777460299 Simplifying r + 1 = -2.777460299 Reorder the terms: 1 + r = -2.777460299 Solving 1 + r = -2.777460299 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 = -2.777460299 + -1 Combine like terms: 1 + -1 = 0 0 + r = -2.777460299 + -1 r = -2.777460299 + -1 Combine like terms: -2.777460299 + -1 = -3.777460299 r = -3.777460299 Simplifying r = -3.777460299

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.777460299, -3.777460299}

See similar equations:

| 5(7+3x)=-130 | | 12(x-7)+4=8y | | 6v+11-15v=-5 | | 20(a+7+9b)= | | 1.10(7x-5)=35 | | 6(-4+5x)=-24 | | 5(3+4x)-9= | | -3.5n-3.7=64.434 | | (x+2)(y^2+2y-12)=0 | | 8-2b=-3b+4 | | 5(-6x+3)=255 | | (-6x+3)=255 | | -4x+5=3(x-3) | | 4t^3-24t^2+36t+60=0 | | -2(6x-3)=-42 | | 4x+3.9=5.78 | | 2x^2+2y^2=3 | | 150000000000/300000000= | | 7y+6=y | | 3r+7s-3(5r-5s)= | | -3+3n=1+4n | | 7y+6=4 | | n+2(n+1)= | | -x+19-8x+2x=17 | | 3x+2(x-1)=4x+6-2x | | 4(x-3)+1=32 | | E=I(R+r)solveR | | 0.4(x+50)+0.6x=45 | | 24(x+1)=-6(4-x)+18x | | q^2+-7.5q+25=-1q^2+-7.5q | | 8y=23+3(2y-7) | | 1.1(x-2)-4.5=2.1(x-1) |

Equations solver categories