6x^2+14x+7=0

Simple and best practice solution for 6x^2+14x+7=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 6x^2+14x+7=0 equation:


Simplifying
6x2 + 14x + 7 = 0

Reorder the terms:
7 + 14x + 6x2 = 0

Solving
7 + 14x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
1.166666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + 2.333333333x + -1.166666667 + x2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + 2.333333333x + x2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + -1.166666667
2.333333333x + x2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
2.333333333x + x2 = -1.166666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = -1.166666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -1.166666667 + 1.361111112

Combine like terms: -1.166666667 + 1.361111112 = 0.194444445
1.361111112 + 2.333333333x + x2 = 0.194444445

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 0.194444445

Calculate the square root of the right side: 0.440958552

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 0.440958552 and -0.440958552.

Subproblem 1

x + 1.166666667 = 0.440958552 Simplifying x + 1.166666667 = 0.440958552 Reorder the terms: 1.166666667 + x = 0.440958552 Solving 1.166666667 + x = 0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 0.440958552 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 0.440958552 + -1.166666667 x = 0.440958552 + -1.166666667 Combine like terms: 0.440958552 + -1.166666667 = -0.725708115 x = -0.725708115 Simplifying x = -0.725708115

Subproblem 2

x + 1.166666667 = -0.440958552 Simplifying x + 1.166666667 = -0.440958552 Reorder the terms: 1.166666667 + x = -0.440958552 Solving 1.166666667 + x = -0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -0.440958552 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -0.440958552 + -1.166666667 x = -0.440958552 + -1.166666667 Combine like terms: -0.440958552 + -1.166666667 = -1.607625219 x = -1.607625219 Simplifying x = -1.607625219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.725708115, -1.607625219}

See similar equations:

| 4(5x+20)=100 | | 6x+7=5(x+5)+2 | | 5x^2+20x-7=0 | | 2x-6=2x-3 | | 3=8x+7 | | 7/8y-8=6 | | 5y+6-y-9= | | x-8/9=-7/9 | | -11/12x+7/12=-1/6 | | x+2.45=-3.22 | | 1/4x-2/3=-5/6 | | 2n/3-3/7=19/21 | | -3n-4n+3= | | 6x+1=5(x-2)-9 | | (-8)-(-4)= | | (3x^3-4x^2+5x)(-x^2y)= | | 17=3cp-5 | | 12n-5=6n-11 | | -4.5x+4=0.6 | | 15845000=.008x^2+10.845 | | (1/3-7i)(1/3+7i) | | (5x-4y)-(3x+7y)= | | 5x^2(-5x^2+3x-9)= | | 5x^2(-5x^2+33-9)= | | -4(x-w)-4(2w-x)= | | (-2.2)+0.3z=3-0.5z-0.8z | | 6x-7=-5 | | 4x-5=20x+3 | | f(6)=3y^2+7y-2 | | 525+0.21+x=585+0.13x | | 525+0.12x=585+0.13x | | (d^2)-6d=14 |

Equations solver categories