13x^2-20x+1=0

Simple and best practice solution for 13x^2-20x+1=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 13x^2-20x+1=0 equation:


Simplifying
13x2 + -20x + 1 = 0

Reorder the terms:
1 + -20x + 13x2 = 0

Solving
1 + -20x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
0.07692307692 + -1.538461538x + x2 = 0

Move the constant term to the right:

Add '-0.07692307692' to each side of the equation.
0.07692307692 + -1.538461538x + -0.07692307692 + x2 = 0 + -0.07692307692

Reorder the terms:
0.07692307692 + -0.07692307692 + -1.538461538x + x2 = 0 + -0.07692307692

Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000
0.00000000000 + -1.538461538x + x2 = 0 + -0.07692307692
-1.538461538x + x2 = 0 + -0.07692307692

Combine like terms: 0 + -0.07692307692 = -0.07692307692
-1.538461538x + x2 = -0.07692307692

The x term is -1.538461538x.  Take half its coefficient (-0.769230769).
Square it (0.5917159760) and add it to both sides.

Add '0.5917159760' to each side of the equation.
-1.538461538x + 0.5917159760 + x2 = -0.07692307692 + 0.5917159760

Reorder the terms:
0.5917159760 + -1.538461538x + x2 = -0.07692307692 + 0.5917159760

Combine like terms: -0.07692307692 + 0.5917159760 = 0.51479289908
0.5917159760 + -1.538461538x + x2 = 0.51479289908

Factor a perfect square on the left side:
(x + -0.769230769)(x + -0.769230769) = 0.51479289908

Calculate the square root of the right side: 0.717490696

Break this problem into two subproblems by setting 
(x + -0.769230769) equal to 0.717490696 and -0.717490696.

Subproblem 1

x + -0.769230769 = 0.717490696 Simplifying x + -0.769230769 = 0.717490696 Reorder the terms: -0.769230769 + x = 0.717490696 Solving -0.769230769 + x = 0.717490696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.769230769' to each side of the equation. -0.769230769 + 0.769230769 + x = 0.717490696 + 0.769230769 Combine like terms: -0.769230769 + 0.769230769 = 0.000000000 0.000000000 + x = 0.717490696 + 0.769230769 x = 0.717490696 + 0.769230769 Combine like terms: 0.717490696 + 0.769230769 = 1.486721465 x = 1.486721465 Simplifying x = 1.486721465

Subproblem 2

x + -0.769230769 = -0.717490696 Simplifying x + -0.769230769 = -0.717490696 Reorder the terms: -0.769230769 + x = -0.717490696 Solving -0.769230769 + x = -0.717490696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.769230769' to each side of the equation. -0.769230769 + 0.769230769 + x = -0.717490696 + 0.769230769 Combine like terms: -0.769230769 + 0.769230769 = 0.000000000 0.000000000 + x = -0.717490696 + 0.769230769 x = -0.717490696 + 0.769230769 Combine like terms: -0.717490696 + 0.769230769 = 0.051740073 x = 0.051740073 Simplifying x = 0.051740073

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.486721465, 0.051740073}

See similar equations:

| 8p+15-p=102 | | y=-9/10x+34 | | -8p^2-24p=0 | | g/2-g-4/4=7/4 | | -[8z-(11z+4)]=4+(2z+10) | | 4Y-4Y=-24-24 | | 8u^7+12u^6-36u^5=0 | | -0.7(-9.2857)-2.9y=-6.5 | | (24+4Y)-4Y=-24 | | -2p-6(5-2p)=5(p-5)-45 | | -0.7*9.2857-2.9y=-6.5 | | X-4(3y)+5=25 | | 2x+5y-4=14 | | 2(12+2y)-4Y=-24 | | -0.7x-2.9y=-6.5 | | 3y=-5x+2 | | -71-5x=13-8x | | 8x^2+27x=7 | | 8(2-(2x-5))=2(8-3x) | | .99x+1.29y=15.36 | | 8+14=2 | | 5/7+4/9=5/6 | | 13b-13/7b-2 | | 3*m*2*p= | | Q=80+12Q | | 15X+28=6X+280 | | x/2+x/3=25/2 | | [5x+13]=-7 | | 1/10+x=5/6x-4/5 | | C(Q)=80+12Q | | 1/10+k=7/8k-4/5 | | y=50 |

Equations solver categories