14z^4-70z^3+35z^2=0

Simple and best practice solution for 14z^4-70z^3+35z^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 14z^4-70z^3+35z^2=0 equation:


Simplifying
14z4 + -70z3 + 35z2 = 0

Reorder the terms:
35z2 + -70z3 + 14z4 = 0

Solving
35z2 + -70z3 + 14z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7z2'.
7z2(5 + -10z + 2z2) = 0

Ignore the factor 7.

Subproblem 1

Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}

Subproblem 2

Set the factor '(5 + -10z + 2z2)' equal to zero and attempt to solve: Simplifying 5 + -10z + 2z2 = 0 Solving 5 + -10z + 2z2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -5z + z2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5z + -2.5 + z2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5z + z2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5z + z2 = 0 + -2.5 -5z + z2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5z + z2 = -2.5 The z term is -5z. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5z + 6.25 + z2 = -2.5 + 6.25 Reorder the terms: 6.25 + -5z + z2 = -2.5 + 6.25 Combine like terms: -2.5 + 6.25 = 3.75 6.25 + -5z + z2 = 3.75 Factor a perfect square on the left side: (z + -2.5)(z + -2.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (z + -2.5) equal to 1.936491673 and -1.936491673.

Subproblem 1

z + -2.5 = 1.936491673 Simplifying z + -2.5 = 1.936491673 Reorder the terms: -2.5 + z = 1.936491673 Solving -2.5 + z = 1.936491673 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = 1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = 1.936491673 + 2.5 z = 1.936491673 + 2.5 Combine like terms: 1.936491673 + 2.5 = 4.436491673 z = 4.436491673 Simplifying z = 4.436491673

Subproblem 2

z + -2.5 = -1.936491673 Simplifying z + -2.5 = -1.936491673 Reorder the terms: -2.5 + z = -1.936491673 Solving -2.5 + z = -1.936491673 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = -1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = -1.936491673 + 2.5 z = -1.936491673 + 2.5 Combine like terms: -1.936491673 + 2.5 = 0.563508327 z = 0.563508327 Simplifying z = 0.563508327

Solution

The solution to the problem is based on the solutions from the subproblems. z = {4.436491673, 0.563508327}

Solution

z = {0, 4.436491673, 0.563508327}

See similar equations:

| 90-30+10x=20 | | 8.7a+14=109.7 | | 12/25÷2/5 | | -3x^3+28x^2-55x-50=0 | | 3x+4y+5z=D | | 2xy(5yz)+x= | | 1/8(x-16 | | 4x^2-1/-2x-5 | | 16-3x(x-3)=9x-176 | | 8xy+-3xy= | | 7x=35-2x | | 0.6666667(5x+1)=4(2-4x)+12 | | 6x+9x=-6-12 | | 3=ln(3x+3) | | 7x+1738=37 | | 5(z+3)=4z | | s-10=20.57 | | Y=4(x-z) | | 1-1=1b | | 5=1+12w | | 9x-3x+2x=60-20 | | 13-4b=-19 | | -2z-4z=-19+4 | | x/43-87=-73 | | 8y+7=y+12 | | 5x-2x=100-1 | | 6r+1*5r-6= | | 12-5w=2 | | -4x-5x=-17+1 | | 238b-828(34b+82738)=81738 | | X-11/X-1=3-2X/X-1 | | h=-16t^2+50t+3 |

Equations solver categories