3x^2-10x-3=0

Simple and best practice solution for 3x^2-10x-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 3x^2-10x-3=0 equation:


Simplifying
3x2 + -10x + -3 = 0

Reorder the terms:
-3 + -10x + 3x2 = 0

Solving
-3 + -10x + 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 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3.333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.333333333x + x2 = 0 + 1
-3.333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.333333333x + x2 = 1

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 1 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 1 + 2.777777779

Combine like terms: 1 + 2.777777779 = 3.777777779
2.777777779 + -3.333333333x + x2 = 3.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 3.777777779

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 1.943650632 and -1.943650632.

Subproblem 1

x + -1.666666667 = 1.943650632 Simplifying x + -1.666666667 = 1.943650632 Reorder the terms: -1.666666667 + x = 1.943650632 Solving -1.666666667 + x = 1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.943650632 + 1.666666667 x = 1.943650632 + 1.666666667 Combine like terms: 1.943650632 + 1.666666667 = 3.610317299 x = 3.610317299 Simplifying x = 3.610317299

Subproblem 2

x + -1.666666667 = -1.943650632 Simplifying x + -1.666666667 = -1.943650632 Reorder the terms: -1.666666667 + x = -1.943650632 Solving -1.666666667 + x = -1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.943650632 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.943650632 + 1.666666667 x = -1.943650632 + 1.666666667 Combine like terms: -1.943650632 + 1.666666667 = -0.276983965 x = -0.276983965 Simplifying x = -0.276983965

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.610317299, -0.276983965}

See similar equations:

| x^2+10x+125=0 | | 1/4-31/4 | | 2r+5s=2 | | -4-y=-77 | | -13+y=-4 | | -21=24x | | -7+1/5y=7 | | 12x+-2x^2=24-4x | | 1/4y=8 | | 6+1/6y=-7 | | -.75+-.75= | | -30(-5)+31= | | 4x^3(x-3)-2x(x-3)=0 | | 4p=-p-20 | | -2(x+7)=42 | | 64*9.5= | | 4x^2+48=32x | | 18(2)+-40= | | x(x+3)-8(x+3)=0 | | 20(-3)-13= | | 14k=126 | | 2y+14=42-5y | | 2x+7y=14fory | | (3x-1)2-(2x+3)2=0 | | x^2+y^2-6x+8y=0 | | 5r^5t^5-10r^6t^4=0 | | x(2x+11)=-12 | | 52=-4x | | -13x+26=1-8x | | 67x-09=76x | | -4x+19=-1 | | 3x-2-7x=4x+6 |

Equations solver categories