13z^2+6z=35

Simple and best practice solution for 13z^2+6z=35 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 13z^2+6z=35 equation:


Simplifying
13z2 + 6z = 35

Reorder the terms:
6z + 13z2 = 35

Solving
6z + 13z2 = 35

Solving for variable 'z'.

Reorder the terms:
-35 + 6z + 13z2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 6z + 13z2 = 0

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

Divide each side by '13'.
-2.692307692 + 0.4615384615z + z2 = 0

Move the constant term to the right:

Add '2.692307692' to each side of the equation.
-2.692307692 + 0.4615384615z + 2.692307692 + z2 = 0 + 2.692307692

Reorder the terms:
-2.692307692 + 2.692307692 + 0.4615384615z + z2 = 0 + 2.692307692

Combine like terms: -2.692307692 + 2.692307692 = 0.000000000
0.000000000 + 0.4615384615z + z2 = 0 + 2.692307692
0.4615384615z + z2 = 0 + 2.692307692

Combine like terms: 0 + 2.692307692 = 2.692307692
0.4615384615z + z2 = 2.692307692

The z term is 0.4615384615z.  Take half its coefficient (0.2307692308).
Square it (0.05325443788) and add it to both sides.

Add '0.05325443788' to each side of the equation.
0.4615384615z + 0.05325443788 + z2 = 2.692307692 + 0.05325443788

Reorder the terms:
0.05325443788 + 0.4615384615z + z2 = 2.692307692 + 0.05325443788

Combine like terms: 2.692307692 + 0.05325443788 = 2.74556212988
0.05325443788 + 0.4615384615z + z2 = 2.74556212988

Factor a perfect square on the left side:
(z + 0.2307692308)(z + 0.2307692308) = 2.74556212988

Calculate the square root of the right side: 1.656973787

Break this problem into two subproblems by setting 
(z + 0.2307692308) equal to 1.656973787 and -1.656973787.

Subproblem 1

z + 0.2307692308 = 1.656973787 Simplifying z + 0.2307692308 = 1.656973787 Reorder the terms: 0.2307692308 + z = 1.656973787 Solving 0.2307692308 + z = 1.656973787 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.2307692308' to each side of the equation. 0.2307692308 + -0.2307692308 + z = 1.656973787 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + z = 1.656973787 + -0.2307692308 z = 1.656973787 + -0.2307692308 Combine like terms: 1.656973787 + -0.2307692308 = 1.4262045562 z = 1.4262045562 Simplifying z = 1.4262045562

Subproblem 2

z + 0.2307692308 = -1.656973787 Simplifying z + 0.2307692308 = -1.656973787 Reorder the terms: 0.2307692308 + z = -1.656973787 Solving 0.2307692308 + z = -1.656973787 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.2307692308' to each side of the equation. 0.2307692308 + -0.2307692308 + z = -1.656973787 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + z = -1.656973787 + -0.2307692308 z = -1.656973787 + -0.2307692308 Combine like terms: -1.656973787 + -0.2307692308 = -1.8877430178 z = -1.8877430178 Simplifying z = -1.8877430178

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.4262045562, -1.8877430178}

See similar equations:

| 13z^2+6=35 | | 2x+3=4+2x | | 5x-1=69 | | 6x+9=9x-19 | | 4x^2-7xy-2y^2=0 | | 64x^3+125= | | Y+4=2x+4 | | 5(x-6)=-48-4x | | 4x^2-26x+26=0 | | X+2x+5+4x+1=20 | | 2x^2-x-120=0 | | 3x+55=8x-62 | | 3=2y+3 | | 8x+60=2x+120 | | 118-6x=21x+22 | | 9x+177=4x+172 | | 7x+15=2x+85 | | 2x+89=4x-17 | | .5s=4s-21 | | 3x^2-41x=-110 | | 149-4x=32x+17 | | 2(x-6)=3(-2x+4) | | 3x+16=13x-64 | | 10=4x+18 | | 9x+5=4x+32 | | 2x+88=6x+24 | | 4(8+x)=68-2x | | 7x+30=2x+60 | | 5x+4=9x+3 | | 5x^2+8x+1=o | | 113-5x=10+23 | | 8x+97=6x+195 |

Equations solver categories