5z^2-15z=9

Simple and best practice solution for 5z^2-15z=9 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 5z^2-15z=9 equation:


Simplifying
5z2 + -15z = 9

Reorder the terms:
-15z + 5z2 = 9

Solving
-15z + 5z2 = 9

Solving for variable 'z'.

Reorder the terms:
-9 + -15z + 5z2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -15z + 5z2 = 0

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

Divide each side by '5'.
-1.8 + -3z + z2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -3z + 1.8 + z2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -3z + z2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -3z + z2 = 0 + 1.8
-3z + z2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-3z + z2 = 1.8

The z term is -3z.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3z + 2.25 + z2 = 1.8 + 2.25

Reorder the terms:
2.25 + -3z + z2 = 1.8 + 2.25

Combine like terms: 1.8 + 2.25 = 4.05
2.25 + -3z + z2 = 4.05

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = 4.05

Calculate the square root of the right side: 2.01246118

Break this problem into two subproblems by setting 
(z + -1.5) equal to 2.01246118 and -2.01246118.

Subproblem 1

z + -1.5 = 2.01246118 Simplifying z + -1.5 = 2.01246118 Reorder the terms: -1.5 + z = 2.01246118 Solving -1.5 + z = 2.01246118 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = 2.01246118 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = 2.01246118 + 1.5 z = 2.01246118 + 1.5 Combine like terms: 2.01246118 + 1.5 = 3.51246118 z = 3.51246118 Simplifying z = 3.51246118

Subproblem 2

z + -1.5 = -2.01246118 Simplifying z + -1.5 = -2.01246118 Reorder the terms: -1.5 + z = -2.01246118 Solving -1.5 + z = -2.01246118 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = -2.01246118 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = -2.01246118 + 1.5 z = -2.01246118 + 1.5 Combine like terms: -2.01246118 + 1.5 = -0.51246118 z = -0.51246118 Simplifying z = -0.51246118

Solution

The solution to the problem is based on the solutions from the subproblems. z = {3.51246118, -0.51246118}

See similar equations:

| 5x^2-52x+32=0 | | 2a=-5x+4 | | M-8m=63 | | 57x+y=21 | | 2ln(x-2)=ln(-5x+16) | | 6x^2+8x+30y-780=0 | | 4x=x(-2)-24 | | lnx-ln(x+1)=ln(x-2) | | 6+2g=15 | | m(3x-n)+6=n(1-x)+2 | | 57x+21y=18 | | 9x^5=2x-16 | | 2/3x+4/5x=80 | | 2(5a-x)-ax=b-1 | | -2(4n+2)=14 | | ydx+x(lnx-lny-1)dy=0 | | 14x-68=11x+22 | | 12x-152=-3x+178 | | 7+x-5=7 | | ax-7=bx+2 | | 3+9=39 | | 8x^2+4x=-1 | | 15=-4x+1 | | e^10x=0 | | -8x-63=29-12x | | -3x-17=18-2x | | -11x-31=31-13x | | 11+y-5=6 | | 11x-20=13x+6 | | -50-0.25d=-100 | | -50-0.25d=-75 | | 6x^2+8x+30y=0 |

Equations solver categories