6x^2+10x=1

Simple and best practice solution for 6x^2+10x=1 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 6x^2+10x=1 equation: 


Simplifying
6x2 + 10x = 1

Reorder the terms:
10x + 6x2 = 1

Solving
10x + 6x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 10x + 6x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 10x + 6x2 = 0

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

Divide each side by '6'.
-0.1666666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 1.666666667x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 1.666666667x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 1.666666667x + x2 = 0 + 0.1666666667
1.666666667x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
1.666666667x + x2 = 0.1666666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 0.1666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 0.1666666667 + 0.6944444447

Combine like terms: 0.1666666667 + 0.6944444447 = 0.8611111114
0.6944444447 + 1.666666667x + x2 = 0.8611111114

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 0.8611111114

Calculate the square root of the right side: 0.927960727

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 0.927960727 and -0.927960727.


Subproblem 1
x + 0.8333333335 = 0.927960727

Simplifying
x + 0.8333333335 = 0.927960727

Reorder the terms:
0.8333333335 + x = 0.927960727

Solving
0.8333333335 + x = 0.927960727

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 0.927960727 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 0.927960727 + -0.8333333335
x = 0.927960727 + -0.8333333335

Combine like terms: 0.927960727 + -0.8333333335 = 0.0946273935
x = 0.0946273935

Simplifying
x = 0.0946273935


Subproblem 2
x + 0.8333333335 = -0.927960727

Simplifying
x + 0.8333333335 = -0.927960727

Reorder the terms:
0.8333333335 + x = -0.927960727

Solving
0.8333333335 + x = -0.927960727

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -0.927960727 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -0.927960727 + -0.8333333335
x = -0.927960727 + -0.8333333335

Combine like terms: -0.927960727 + -0.8333333335 = -1.7612940605
x = -1.7612940605

Simplifying
x = -1.7612940605


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0946273935, -1.7612940605}

See similar equations:

| z/8-4=19 | | 9(x+6)+5(x+6)=5x-5 | | [sqrt[u-8]]=5 | | 5t=6t | | -s=8+7s | | 11x+9=97 | | -5x+44=4 | | 6u=-3+5u | | 4=5.6/X | | 4m-15=45 | | 3b+5=-4b-9 | | 2x^3-9x-5x=0 | | 9(3+v)+37v=10v | | 6x+19x=225 | | x*x-7x-54=0 | | n=280(1-.25) | | 9(3+v)+37v=10 | | (1[2+z]1)(1[5z-4]1)=0 | | -30=42+c | | 7v=1+8v | | 3(x-4)=1-(4x-15) | | 8m-15+7m=145 | | 4-2x=x-5 | | 9f=10+8f | | -4x+9y=-22 | | 5-4m=-5m | | -b=-10b-9 | | -4(4-5y)=11y+20 | | 6x+9x=15x | | -2z=-z-6 | | 4x+7x=4x-1x | | -4x+8y=-22 |

Equations solver categories