2k^2+9k=7

Simple and best practice solution for 2k^2+9k=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 2k^2+9k=7 equation:


Simplifying
2k2 + 9k = 7

Reorder the terms:
9k + 2k2 = 7

Solving
9k + 2k2 = 7

Solving for variable 'k'.

Reorder the terms:
-7 + 9k + 2k2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 9k + 2k2 = 0

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

Divide each side by '2'.
-3.5 + 4.5k + k2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 4.5k + 3.5 + k2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 4.5k + k2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 4.5k + k2 = 0 + 3.5
4.5k + k2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
4.5k + k2 = 3.5

The k term is 4.5k.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5k + 5.0625 + k2 = 3.5 + 5.0625

Reorder the terms:
5.0625 + 4.5k + k2 = 3.5 + 5.0625

Combine like terms: 3.5 + 5.0625 = 8.5625
5.0625 + 4.5k + k2 = 8.5625

Factor a perfect square on the left side:
(k + 2.25)(k + 2.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(k + 2.25) equal to 2.926174978 and -2.926174978.

Subproblem 1

k + 2.25 = 2.926174978 Simplifying k + 2.25 = 2.926174978 Reorder the terms: 2.25 + k = 2.926174978 Solving 2.25 + k = 2.926174978 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + k = 2.926174978 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + k = 2.926174978 + -2.25 k = 2.926174978 + -2.25 Combine like terms: 2.926174978 + -2.25 = 0.676174978 k = 0.676174978 Simplifying k = 0.676174978

Subproblem 2

k + 2.25 = -2.926174978 Simplifying k + 2.25 = -2.926174978 Reorder the terms: 2.25 + k = -2.926174978 Solving 2.25 + k = -2.926174978 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + k = -2.926174978 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + k = -2.926174978 + -2.25 k = -2.926174978 + -2.25 Combine like terms: -2.926174978 + -2.25 = -5.176174978 k = -5.176174978 Simplifying k = -5.176174978

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.676174978, -5.176174978}

See similar equations:

| 5r^2-36r-32=0 | | 253=-2-5(7k+5) | | n^2-13n+50=0 | | -z+4=26 | | -3(8y-5)=4(1-7y)+14 | | Vf=0+0*20 | | 100x+90-x=99 | | 1+3n=1+3n | | 12+2[6+7(x+1)]=0 | | (X+21)+(x+61)+(X+23)=180 | | 1/4x^4-4 | | x-6=4x-2x-9 | | -21x+18x=3(-6-2x) | | 2.9x+4.5x= | | 2b(2a-x)=x(b-a)+a(x+b) | | X^2/3=10 | | 5(x-7)+6=5x-23 | | (2x+3)*(4x+7)=8x^2-5 | | X+(X+55)+(X+38)=180 | | 14/5x−14=4/5x−7/4 | | 12=7m-1+6m | | U=2a+2b | | X+3x-4=5(x+2) | | 6y-2=20 | | 18(2x+6)=6(3x+30) | | 40p-5=-5p-5 | | lne^4/5 | | 3x+7+5x=11+4x+8 | | 2x-6x=-2x | | 26+X^2=90 | | 6x^3+2x^2=10x-8 | | 5.8(x-4)=0.2x+24.8 |

Equations solver categories