13x^2-x-3=0

Simple and best practice solution for 13x^2-x-3=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-x-3=0 equation:


Simplifying
13x2 + -1x + -3 = 0

Reorder the terms:
-3 + -1x + 13x2 = 0

Solving
-3 + -1x + 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'.
-0.2307692308 + -0.07692307692x + x2 = 0

Move the constant term to the right:

Add '0.2307692308' to each side of the equation.
-0.2307692308 + -0.07692307692x + 0.2307692308 + x2 = 0 + 0.2307692308

Reorder the terms:
-0.2307692308 + 0.2307692308 + -0.07692307692x + x2 = 0 + 0.2307692308

Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000
0.0000000000 + -0.07692307692x + x2 = 0 + 0.2307692308
-0.07692307692x + x2 = 0 + 0.2307692308

Combine like terms: 0 + 0.2307692308 = 0.2307692308
-0.07692307692x + x2 = 0.2307692308

The x term is -0.07692307692x.  Take half its coefficient (-0.03846153846).
Square it (0.001479289941) and add it to both sides.

Add '0.001479289941' to each side of the equation.
-0.07692307692x + 0.001479289941 + x2 = 0.2307692308 + 0.001479289941

Reorder the terms:
0.001479289941 + -0.07692307692x + x2 = 0.2307692308 + 0.001479289941

Combine like terms: 0.2307692308 + 0.001479289941 = 0.232248520741
0.001479289941 + -0.07692307692x + x2 = 0.232248520741

Factor a perfect square on the left side:
(x + -0.03846153846)(x + -0.03846153846) = 0.232248520741

Calculate the square root of the right side: 0.481921696

Break this problem into two subproblems by setting 
(x + -0.03846153846) equal to 0.481921696 and -0.481921696.

Subproblem 1

x + -0.03846153846 = 0.481921696 Simplifying x + -0.03846153846 = 0.481921696 Reorder the terms: -0.03846153846 + x = 0.481921696 Solving -0.03846153846 + x = 0.481921696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + x = 0.481921696 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + x = 0.481921696 + 0.03846153846 x = 0.481921696 + 0.03846153846 Combine like terms: 0.481921696 + 0.03846153846 = 0.52038323446 x = 0.52038323446 Simplifying x = 0.52038323446

Subproblem 2

x + -0.03846153846 = -0.481921696 Simplifying x + -0.03846153846 = -0.481921696 Reorder the terms: -0.03846153846 + x = -0.481921696 Solving -0.03846153846 + x = -0.481921696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + x = -0.481921696 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + x = -0.481921696 + 0.03846153846 x = -0.481921696 + 0.03846153846 Combine like terms: -0.481921696 + 0.03846153846 = -0.44346015754 x = -0.44346015754 Simplifying x = -0.44346015754

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.52038323446, -0.44346015754}

See similar equations:

| 5(2n-5)-3=2(3n-4)-8 | | 5x=10.2 | | 4x-0.4=5x | | -2x+4(4+x)=2x-4(6-3x) | | 9x^2-12x+30=0 | | 2a-9=4(3a+1)-5 | | y^2-y=-6y+6 | | 7-5x=9-3x | | -3z+2z=15-8 | | 6(k-3)-(k-4)=-(k+6)-1 | | 3y(1-2y)(y-2)=0 | | 5x-12=2a+6 | | -6x+2x+3=-4x-6 | | 4x+19+8x+17=180 | | 0.6x+0.14-0.2x=0.38 | | 6y+4y=9y+2 | | 3k-7/5=16 | | 2x+18+3x+22=180 | | -6x+2x+3=-4x+3 | | -x+8=-(8-x) | | 6x+10+4x+30=90 | | -6(k+1)-k-6=-7(k+5)+23 | | 4*y-70=12*y+2 | | 5x^2-2=-12 | | x=16-9*x | | 4t^2=6t | | 3x+48=6x+24 | | x^2+ax+4=0 | | (3x+2)-(x+4)=7 | | 11-20x-25y= | | 2x(x+1)=1 | | 4x+5-8+10=2x-12 |

Equations solver categories