21x^2-2x-1=0

Simple and best practice solution for 21x^2-2x-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 21x^2-2x-1=0 equation:


Simplifying
21x2 + -2x + -1 = 0

Reorder the terms:
-1 + -2x + 21x2 = 0

Solving
-1 + -2x + 21x2 = 0

Solving for variable 'x'.

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

Divide each side by '21'.
-0.04761904762 + -0.09523809524x + x2 = 0

Move the constant term to the right:

Add '0.04761904762' to each side of the equation.
-0.04761904762 + -0.09523809524x + 0.04761904762 + x2 = 0 + 0.04761904762

Reorder the terms:
-0.04761904762 + 0.04761904762 + -0.09523809524x + x2 = 0 + 0.04761904762

Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000
0.00000000000 + -0.09523809524x + x2 = 0 + 0.04761904762
-0.09523809524x + x2 = 0 + 0.04761904762

Combine like terms: 0 + 0.04761904762 = 0.04761904762
-0.09523809524x + x2 = 0.04761904762

The x term is -0.09523809524x.  Take half its coefficient (-0.04761904762).
Square it (0.002267573696) and add it to both sides.

Add '0.002267573696' to each side of the equation.
-0.09523809524x + 0.002267573696 + x2 = 0.04761904762 + 0.002267573696

Reorder the terms:
0.002267573696 + -0.09523809524x + x2 = 0.04761904762 + 0.002267573696

Combine like terms: 0.04761904762 + 0.002267573696 = 0.049886621316
0.002267573696 + -0.09523809524x + x2 = 0.049886621316

Factor a perfect square on the left side:
(x + -0.04761904762)(x + -0.04761904762) = 0.049886621316

Calculate the square root of the right side: 0.223353131

Break this problem into two subproblems by setting 
(x + -0.04761904762) equal to 0.223353131 and -0.223353131.

Subproblem 1

x + -0.04761904762 = 0.223353131 Simplifying x + -0.04761904762 = 0.223353131 Reorder the terms: -0.04761904762 + x = 0.223353131 Solving -0.04761904762 + x = 0.223353131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.04761904762 + x = 0.223353131 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + x = 0.223353131 + 0.04761904762 x = 0.223353131 + 0.04761904762 Combine like terms: 0.223353131 + 0.04761904762 = 0.27097217862 x = 0.27097217862 Simplifying x = 0.27097217862

Subproblem 2

x + -0.04761904762 = -0.223353131 Simplifying x + -0.04761904762 = -0.223353131 Reorder the terms: -0.04761904762 + x = -0.223353131 Solving -0.04761904762 + x = -0.223353131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.04761904762 + x = -0.223353131 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + x = -0.223353131 + 0.04761904762 x = -0.223353131 + 0.04761904762 Combine like terms: -0.223353131 + 0.04761904762 = -0.17573408338 x = -0.17573408338 Simplifying x = -0.17573408338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.27097217862, -0.17573408338}

See similar equations:

| 9x+6-6x=3x+6 | | -4(x+1)+5x=15 | | n+5=-25 | | 10-6k=48 | | 3(x+9)=27 | | x^2-13=12 | | 17*.08+x=31.80 | | 5x+4x=122 | | 6x-3x+2=-0 | | 3x^2+4=22 | | -16-6x=4x+15 | | x+2=-x+6 | | -3(x-7)+4=25 | | x^2(x+1)*(x-1)= | | 9(2x+8)=16-(x+1) | | 15x-8x+7=-42 | | 10x+2=3(3x-2)+8 | | 17-3x=x+1 | | 3x^4+2x^3+3x^2+2x=0 | | -42-3x=2x+10 | | 3a-6+7a=6a+12 | | -16x^2+160x+30=0 | | 2x^2+16xy+32y^2=0 | | -8c=-32 | | 4.50(180-y)+8.25y=1222.50 | | 5(4X-7)-(2X-5)3=-34 | | -7d+1=15 | | 5-2(2x+1)=7 | | 8n-20=6-5n | | 10x-x+4=-5 | | -28=2(2x-2)-4 | | 12x^3-4x^2+21x-7=0 |

Equations solver categories