3*x^2-14*x-3=0

Simple and best practice solution for 3*x^2-14*x-3=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 3*x^2-14*x-3=0 equation:


Simplifying
3x2 + -14x + -3 = 0

Reorder the terms:
-3 + -14x + 3x2 = 0

Solving
-3 + -14x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-1 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.666666667x + x2 = 0 + 1
-4.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.666666667x + x2 = 1

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 1 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 1 + 5.444444448

Combine like terms: 1 + 5.444444448 = 6.444444448
5.444444448 + -4.666666667x + x2 = 6.444444448

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 6.444444448

Calculate the square root of the right side: 2.538591036

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.538591036 and -2.538591036.

Subproblem 1

x + -2.333333334 = 2.538591036 Simplifying x + -2.333333334 = 2.538591036 Reorder the terms: -2.333333334 + x = 2.538591036 Solving -2.333333334 + x = 2.538591036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.538591036 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.538591036 + 2.333333334 x = 2.538591036 + 2.333333334 Combine like terms: 2.538591036 + 2.333333334 = 4.87192437 x = 4.87192437 Simplifying x = 4.87192437

Subproblem 2

x + -2.333333334 = -2.538591036 Simplifying x + -2.333333334 = -2.538591036 Reorder the terms: -2.333333334 + x = -2.538591036 Solving -2.333333334 + x = -2.538591036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.538591036 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.538591036 + 2.333333334 x = -2.538591036 + 2.333333334 Combine like terms: -2.538591036 + 2.333333334 = -0.205257702 x = -0.205257702 Simplifying x = -0.205257702

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.87192437, -0.205257702}

See similar equations:

| 6+x=127 | | x^3-7*x^2-3*x+3=0 | | -10y+9=9y-10 | | 25y+15-16y=7y+1.5y-9 | | -3(4w-1)=8 | | x^2+2xi+11-16i=0 | | 3(1+4b)-b=-85 | | 5y/9/2y=23 | | 4/1^(1/2)-x^(1/2) | | 5x(6-3x)=12 | | -3x-7x/5=5x-(x3) | | 4x+4(2x+10)=100 | | -7/(7/18) | | -4g=-84 | | (2x/5)-(x/2)=40 | | (3/5)x=-6 | | 14-8w=-130 | | (2x/5)-(x/20)=40 | | 3x+3(4x-20)=75 | | 8h=56 | | 7x(4x+3)=5 | | 9+6x=6x+2+4 | | 4t-t-7=2t-4 | | 5(10-3x)=30 | | 16=-5y | | -37=-7x+5(x-5) | | 5x+x-3=5x+6 | | 16y=-5y | | 1/3(8x-1)^2+19=94 | | +111-1-1-1+6+1=23*5 | | +111-1-1-1+6+1=23x | | 13x+6-7=1+8x |

Equations solver categories