12k^2+15k=16k+21

Simple and best practice solution for 12k^2+15k=16k+21 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 12k^2+15k=16k+21 equation:


Simplifying
12k2 + 15k = 16k + 21

Reorder the terms:
15k + 12k2 = 16k + 21

Reorder the terms:
15k + 12k2 = 21 + 16k

Solving
15k + 12k2 = 21 + 16k

Solving for variable 'k'.

Reorder the terms:
-21 + 15k + -16k + 12k2 = 21 + 16k + -21 + -16k

Combine like terms: 15k + -16k = -1k
-21 + -1k + 12k2 = 21 + 16k + -21 + -16k

Reorder the terms:
-21 + -1k + 12k2 = 21 + -21 + 16k + -16k

Combine like terms: 21 + -21 = 0
-21 + -1k + 12k2 = 0 + 16k + -16k
-21 + -1k + 12k2 = 16k + -16k

Combine like terms: 16k + -16k = 0
-21 + -1k + 12k2 = 0

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

Divide each side by '12'.
-1.75 + -0.08333333333k + k2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -0.08333333333k + 1.75 + k2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -0.08333333333k + k2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -0.08333333333k + k2 = 0 + 1.75
-0.08333333333k + k2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-0.08333333333k + k2 = 1.75

The k term is -0.08333333333k.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333k + 0.001736111111 + k2 = 1.75 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333k + k2 = 1.75 + 0.001736111111

Combine like terms: 1.75 + 0.001736111111 = 1.751736111111
0.001736111111 + -0.08333333333k + k2 = 1.751736111111

Factor a perfect square on the left side:
(k + -0.04166666667)(k + -0.04166666667) = 1.751736111111

Calculate the square root of the right side: 1.323531681

Break this problem into two subproblems by setting 
(k + -0.04166666667) equal to 1.323531681 and -1.323531681.

Subproblem 1

k + -0.04166666667 = 1.323531681 Simplifying k + -0.04166666667 = 1.323531681 Reorder the terms: -0.04166666667 + k = 1.323531681 Solving -0.04166666667 + k = 1.323531681 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + k = 1.323531681 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + k = 1.323531681 + 0.04166666667 k = 1.323531681 + 0.04166666667 Combine like terms: 1.323531681 + 0.04166666667 = 1.36519834767 k = 1.36519834767 Simplifying k = 1.36519834767

Subproblem 2

k + -0.04166666667 = -1.323531681 Simplifying k + -0.04166666667 = -1.323531681 Reorder the terms: -0.04166666667 + k = -1.323531681 Solving -0.04166666667 + k = -1.323531681 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + k = -1.323531681 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + k = -1.323531681 + 0.04166666667 k = -1.323531681 + 0.04166666667 Combine like terms: -1.323531681 + 0.04166666667 = -1.28186501433 k = -1.28186501433 Simplifying k = -1.28186501433

Solution

The solution to the problem is based on the solutions from the subproblems. k = {1.36519834767, -1.28186501433}

See similar equations:

| y+3=.33(x-6) | | 9x+14=5x+114 | | x^3+8x^2+5x-14=0 | | 6(x+3)=2y | | (7-6i)+(9+11i)=0 | | 2(3x+7)=x+3(3x-2) | | 2(x-3)=2x+5 | | 4-4=7x+3x | | 10-8(1+x)=7 | | g=139-11t | | 4+4=7x+3x | | 8-7x=44-28x | | 6(x+3)= | | -10x=18-(-12) | | 24x^2+28x+8=0 | | 60-2x=3x+5 | | 12n-23.3=-14n+28.8 | | 5x+12=-123-10x | | 5x+12=123-10x | | -18-2x=12-7x | | 7x-2=2x-9 | | 5(2x-1)-2(3x+2)=6x-17 | | 127-6x=4x-7 | | -2x^2-9x-4=o | | y=(2)x+5x+6 | | 5(2x-1)-2(3x+16)=6x-17 | | -19x-6=9-10x | | 4x+9-3x=14 | | 33x+33x*3=14 | | 2*1075/4754= | | 7x-3=4x+16 | | 15a^2-2a-5=0 |

Equations solver categories