13x^2+10x+1=0

Simple and best practice solution for 13x^2+10x+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+10x+1=0 equation:


Simplifying
13x2 + 10x + 1 = 0

Reorder the terms:
1 + 10x + 13x2 = 0

Solving
1 + 10x + 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 + 0.7692307692x + x2 = 0

Move the constant term to the right:

Add '-0.07692307692' to each side of the equation.
0.07692307692 + 0.7692307692x + -0.07692307692 + x2 = 0 + -0.07692307692

Reorder the terms:
0.07692307692 + -0.07692307692 + 0.7692307692x + x2 = 0 + -0.07692307692

Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000
0.00000000000 + 0.7692307692x + x2 = 0 + -0.07692307692
0.7692307692x + x2 = 0 + -0.07692307692

Combine like terms: 0 + -0.07692307692 = -0.07692307692
0.7692307692x + x2 = -0.07692307692

The x term is 0.7692307692x.  Take half its coefficient (0.3846153846).
Square it (0.1479289941) and add it to both sides.

Add '0.1479289941' to each side of the equation.
0.7692307692x + 0.1479289941 + x2 = -0.07692307692 + 0.1479289941

Reorder the terms:
0.1479289941 + 0.7692307692x + x2 = -0.07692307692 + 0.1479289941

Combine like terms: -0.07692307692 + 0.1479289941 = 0.07100591718
0.1479289941 + 0.7692307692x + x2 = 0.07100591718

Factor a perfect square on the left side:
(x + 0.3846153846)(x + 0.3846153846) = 0.07100591718

Calculate the square root of the right side: 0.266469355

Break this problem into two subproblems by setting 
(x + 0.3846153846) equal to 0.266469355 and -0.266469355.

Subproblem 1

x + 0.3846153846 = 0.266469355 Simplifying x + 0.3846153846 = 0.266469355 Reorder the terms: 0.3846153846 + x = 0.266469355 Solving 0.3846153846 + x = 0.266469355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3846153846' to each side of the equation. 0.3846153846 + -0.3846153846 + x = 0.266469355 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = 0.266469355 + -0.3846153846 x = 0.266469355 + -0.3846153846 Combine like terms: 0.266469355 + -0.3846153846 = -0.1181460296 x = -0.1181460296 Simplifying x = -0.1181460296

Subproblem 2

x + 0.3846153846 = -0.266469355 Simplifying x + 0.3846153846 = -0.266469355 Reorder the terms: 0.3846153846 + x = -0.266469355 Solving 0.3846153846 + x = -0.266469355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3846153846' to each side of the equation. 0.3846153846 + -0.3846153846 + x = -0.266469355 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = -0.266469355 + -0.3846153846 x = -0.266469355 + -0.3846153846 Combine like terms: -0.266469355 + -0.3846153846 = -0.6510847396 x = -0.6510847396 Simplifying x = -0.6510847396

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.1181460296, -0.6510847396}

See similar equations:

| 4r^2-4r+1=0 | | 180-x=3(90-x)-38 | | x/4-1=-x/2+8 | | 5x(x)=90 | | 13x+14=2x-5 | | 2y^2+7y=-5 | | 1-2p+5=4p+6 | | 15x-3=30x-2 | | 15x-3=30x-3 | | -3x+7=-x-1 | | 5x+21=(x^2)+9 | | 3x^2+20x=-32 | | 5x+21=x^2+3 | | 3x^2+20=-32 | | -x^2+5x+12=0 | | 9=5-4x | | 3h^2+4h-224=0 | | 3h^2+4h-14=0 | | 0=3x^2+122x+3721 | | -2x^2=20 | | 10-2(2x+1)=4(x-2) | | 12x+16=4x+8 | | r^4+9y+15=0 | | 5x-23y=7 | | 2t^2+9t-26=0 | | (4x-2)-(-3x-5)=3 | | -2+3x=2x+6+x | | x+0.25x=9 | | 0=-16x^2+64+720 | | 5x-23y=23 | | 12x^3+4x^2+40x=0 | | -7+[-(-9)]= |

Equations solver categories