4x^2-14x-6=0

Simple and best practice solution for 4x^2-14x-6=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 4x^2-14x-6=0 equation: 


Simplifying
4x2 + -14x + -6 = 0

Reorder the terms:
-6 + -14x + 4x2 = 0

Solving
-6 + -14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -7x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-3 + -7x + 2x2 = 0

Solving
-3 + -7x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -3.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -3.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -3.5x + x2 = 0 + 1.5
-3.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-3.5x + x2 = 1.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 1.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 1.5 + 3.0625

Combine like terms: 1.5 + 3.0625 = 4.5625
3.0625 + -3.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.136000936 and -2.136000936.


Subproblem 1
x + -1.75 = 2.136000936

Simplifying
x + -1.75 = 2.136000936

Reorder the terms:
-1.75 + x = 2.136000936

Solving
-1.75 + x = 2.136000936

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.136000936 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.136000936 + 1.75
x = 2.136000936 + 1.75

Combine like terms: 2.136000936 + 1.75 = 3.886000936
x = 3.886000936

Simplifying
x = 3.886000936


Subproblem 2
x + -1.75 = -2.136000936

Simplifying
x + -1.75 = -2.136000936

Reorder the terms:
-1.75 + x = -2.136000936

Solving
-1.75 + x = -2.136000936

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.136000936 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.136000936 + 1.75
x = -2.136000936 + 1.75

Combine like terms: -2.136000936 + 1.75 = -0.386000936
x = -0.386000936

Simplifying
x = -0.386000936


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.886000936, -0.386000936}
Solution
x = {3.886000936, -0.386000936}

See similar equations:

| 4-8=30 | | 3y-2= | | -(-7-10x+7y)= | | (-4)(5m+2)-3m= | | 4x+11=-28-9x | | -142+4x=-9x+105 | | 7x-84=4x-9 | | -3*1.6+2=-7 | | 4(y+1)=10 | | 64-5x=13x+16 | | 3c^2+9c-8+c-5+12c^2-6c+10= | | 25m-1=0 | | -3c=5 | | 4x^9+32x^8+28x^7= | | r-2r+1=0 | | -3*1.6+2= | | -34-x=44+2x | | 32-12b+b^2= | | 11-8x=33-15x | | -5x-12x=102 | | .75d-.5=2.5 | | -(6x+2-10y)= | | 7j+11=74 | | -1f-13+15f=71 | | 4y-9=0 | | 55-4x=16 | | 2x+7=164x | | 5w+8=3w-5 | | 6d-15=13 | | 1m+29+8m=110 | | 3x-129=-10x+92 | | 38+7t=-3(t+4) |

Equations solver categories