2x^2+6x=1

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


Simplifying
2x2 + 6x = 1

Reorder the terms:
6x + 2x2 = 1

Solving
6x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 6x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 6x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + 3x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3x + x2 = 0 + 0.5
3x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3x + x2 = 0.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 0.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3x + x2 = 2.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

x + 1.5 = 1.658312395 Simplifying x + 1.5 = 1.658312395 Reorder the terms: 1.5 + x = 1.658312395 Solving 1.5 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.658312395 + -1.5 x = 1.658312395 + -1.5 Combine like terms: 1.658312395 + -1.5 = 0.158312395 x = 0.158312395 Simplifying x = 0.158312395

Subproblem 2

x + 1.5 = -1.658312395 Simplifying x + 1.5 = -1.658312395 Reorder the terms: 1.5 + x = -1.658312395 Solving 1.5 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.658312395 + -1.5 x = -1.658312395 + -1.5 Combine like terms: -1.658312395 + -1.5 = -3.158312395 x = -3.158312395 Simplifying x = -3.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.158312395, -3.158312395}

See similar equations:

| 6x^2+16=x(x+42) | | 24=x+1+3x+1 | | 9k-11+2K-7-4k=0 | | 4-4x=-2x+8 | | 8+5x=6x+12 | | 3x-5=-3(5x-7)+2 | | -7(10+k)= | | 32=x+x+7+3x | | 9y+2y-32=0 | | 3b+7=20 | | (x+1)(x+13)=-35 | | -8*1-(3*1+6)=x | | x+4+6=7 | | 6(4z+2)=3(82+4) | | (x-1)(x+13)=-35 | | 4-3n+3=-8 | | 3(t-5)= | | 9=7(4+2) | | -21-13x+10n-5x-3n-10= | | 9x-5=4x+20 | | .75*5.75= | | 4-3n+3=8 | | -2(r-0.50)= | | 3x-5(x-3)=-2+4x-31 | | 5m*30=7m*30 | | 3y=/32-2y | | -3+y=12 | | 4x^2-24x+4=4 | | 2x+5-4x=7 | | 1+3x-3=-8 | | 3(4h+2)=2(h+1) | | -12-13x+10n-5x-3n-10= |

Equations solver categories