12z^2+15z-2=0

Simple and best practice solution for 12z^2+15z-2=0 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 12z^2+15z-2=0 equation:


Simplifying
12z2 + 15z + -2 = 0

Reorder the terms:
-2 + 15z + 12z2 = 0

Solving
-2 + 15z + 12z2 = 0

Solving for variable 'z'.

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

Divide each side by '12'.
-0.1666666667 + 1.25z + z2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 1.25z + 0.1666666667 + z2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 1.25z + z2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 1.25z + z2 = 0 + 0.1666666667
1.25z + z2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
1.25z + z2 = 0.1666666667

The z term is 1.25z.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25z + 0.390625 + z2 = 0.1666666667 + 0.390625

Reorder the terms:
0.390625 + 1.25z + z2 = 0.1666666667 + 0.390625

Combine like terms: 0.1666666667 + 0.390625 = 0.5572916667
0.390625 + 1.25z + z2 = 0.5572916667

Factor a perfect square on the left side:
(z + 0.625)(z + 0.625) = 0.5572916667

Calculate the square root of the right side: 0.746519703

Break this problem into two subproblems by setting 
(z + 0.625) equal to 0.746519703 and -0.746519703.

Subproblem 1

z + 0.625 = 0.746519703 Simplifying z + 0.625 = 0.746519703 Reorder the terms: 0.625 + z = 0.746519703 Solving 0.625 + z = 0.746519703 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + z = 0.746519703 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + z = 0.746519703 + -0.625 z = 0.746519703 + -0.625 Combine like terms: 0.746519703 + -0.625 = 0.121519703 z = 0.121519703 Simplifying z = 0.121519703

Subproblem 2

z + 0.625 = -0.746519703 Simplifying z + 0.625 = -0.746519703 Reorder the terms: 0.625 + z = -0.746519703 Solving 0.625 + z = -0.746519703 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + z = -0.746519703 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + z = -0.746519703 + -0.625 z = -0.746519703 + -0.625 Combine like terms: -0.746519703 + -0.625 = -1.371519703 z = -1.371519703 Simplifying z = -1.371519703

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.121519703, -1.371519703}

See similar equations:

| (x^3-6x^2+6x+1)=0 | | 2x+-24=2(x+32) | | -6p+14=8(7+p) | | 2x-24=x+32 | | 5(3s+1)=170 | | 2(3x)=x+5 | | 4x+34= | | 5(2l+8)=70 | | 3(a-9)=18 | | Ln-8n=0 | | (u+5)*7=63 | | (q-9)*4=12 | | 6x^2+60x+900=0 | | (1[3-v]1)(1[2v+1]1)=0 | | 10x-21=6x-13 | | 4x+34+5x+12+7x-10= | | x+(x+136)=250 | | 42y+7=73 | | -22p-6(4-5p)=6(p-3)-2 | | 0.66x=0.5x+0.33 | | 4+66x=44x+22 | | x+(250-x)=250 | | f(x)=-0.1x^2-0.8x+35 | | 14x-112=8x-58 | | -5(v+4)+2v+5=7v+6 | | 76=12/2w | | x+12=2+y | | -5(6v-7)=-2v-37-4v | | 4/9=m/54 | | 12y+5=9 | | (x-15)(x-3)=0 | | f(-1)+g(-1)= |

Equations solver categories