k(2k+3)=19

Simple and best practice solution for k(2k+3)=19 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 k(2k+3)=19 equation:


Simplifying
k(2k + 3) = 19

Reorder the terms:
k(3 + 2k) = 19
(3 * k + 2k * k) = 19
(3k + 2k2) = 19

Solving
3k + 2k2 = 19

Solving for variable 'k'.

Reorder the terms:
-19 + 3k + 2k2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + 3k + 2k2 = 0

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

Divide each side by '2'.
-9.5 + 1.5k + k2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 1.5k + 9.5 + k2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 1.5k + k2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 1.5k + k2 = 0 + 9.5
1.5k + k2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
1.5k + k2 = 9.5

The k term is 1.5k.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5k + 0.5625 + k2 = 9.5 + 0.5625

Reorder the terms:
0.5625 + 1.5k + k2 = 9.5 + 0.5625

Combine like terms: 9.5 + 0.5625 = 10.0625
0.5625 + 1.5k + k2 = 10.0625

Factor a perfect square on the left side:
(k + 0.75)(k + 0.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(k + 0.75) equal to 3.172144385 and -3.172144385.

Subproblem 1

k + 0.75 = 3.172144385 Simplifying k + 0.75 = 3.172144385 Reorder the terms: 0.75 + k = 3.172144385 Solving 0.75 + k = 3.172144385 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + k = 3.172144385 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + k = 3.172144385 + -0.75 k = 3.172144385 + -0.75 Combine like terms: 3.172144385 + -0.75 = 2.422144385 k = 2.422144385 Simplifying k = 2.422144385

Subproblem 2

k + 0.75 = -3.172144385 Simplifying k + 0.75 = -3.172144385 Reorder the terms: 0.75 + k = -3.172144385 Solving 0.75 + k = -3.172144385 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + k = -3.172144385 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + k = -3.172144385 + -0.75 k = -3.172144385 + -0.75 Combine like terms: -3.172144385 + -0.75 = -3.922144385 k = -3.922144385 Simplifying k = -3.922144385

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.422144385, -3.922144385}

See similar equations:

| (-3x-6)(-8x+9)+6x+12=0 | | m(a-3b)=2t | | -3x^2(-4x^2+x-7)= | | ax+b=2m | | 4(2c-6)=3(c+7) | | y^2-2xy-(3x^2+5)=0 | | 8x=18+5y | | Cos(x+45)=0 | | 3+35=20x+30 | | 5x(4x+1)=0 | | (3x+7)(2x-9)=0 | | 12xy-12x=0 | | 1-a*z-a^2*z^2=0 | | 3p+2z+1=p-(-22-1) | | 34.969x+36.966(x-1)=35.453 | | 5(2w+3)-6(w+2)= | | 5(3x-8)-2=5(x-3)+43 | | 6a+9whena=8 | | x(x-15+2x)+18=0 | | 3x^2+4x=87 | | 25x+40x+16=0 | | -4x+6+8x-4= | | -6p+-15+-3p+21= | | 3x+9=-10.5 | | X-2-5x-10= | | 5x-10-x-2= | | 2x-8-8x+2= | | 11x^2+121x+308= | | 8x+2-2x-8= | | 5x-10+9x-8= | | 950g=1kg | | 950g=1 |

Equations solver categories