3x^2+13x-3=0

Simple and best practice solution for 3x^2+13x-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+13x-3=0 equation:


Simplifying
3x2 + 13x + -3 = 0

Reorder the terms:
-3 + 13x + 3x2 = 0

Solving
-3 + 13x + 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 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4.333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4.333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4.333333333x + x2 = 0 + 1
4.333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4.333333333x + x2 = 1

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 1 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 1 + 4.694444446

Combine like terms: 1 + 4.694444446 = 5.694444446
4.694444446 + 4.333333333x + x2 = 5.694444446

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 5.694444446

Calculate the square root of the right side: 2.386303511

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 2.386303511 and -2.386303511.

Subproblem 1

x + 2.166666667 = 2.386303511 Simplifying x + 2.166666667 = 2.386303511 Reorder the terms: 2.166666667 + x = 2.386303511 Solving 2.166666667 + x = 2.386303511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 2.386303511 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 2.386303511 + -2.166666667 x = 2.386303511 + -2.166666667 Combine like terms: 2.386303511 + -2.166666667 = 0.219636844 x = 0.219636844 Simplifying x = 0.219636844

Subproblem 2

x + 2.166666667 = -2.386303511 Simplifying x + 2.166666667 = -2.386303511 Reorder the terms: 2.166666667 + x = -2.386303511 Solving 2.166666667 + x = -2.386303511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -2.386303511 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -2.386303511 + -2.166666667 x = -2.386303511 + -2.166666667 Combine like terms: -2.386303511 + -2.166666667 = -4.552970178 x = -4.552970178 Simplifying x = -4.552970178

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.219636844, -4.552970178}

See similar equations:

| -9/4=-3u | | -4/5u=8 | | 4+5x=0 | | A=(21)(3.14)(m)(m) | | 24x^2-281x-84=0 | | 24x^2+281x-84=0 | | 24x^2+274x-84=0 | | 3y+6-10=89 | | -22=-6+4x | | (t-5)/3(t-5)/3=49 | | 2-(120/x^2)=0 | | 2-(120/x^2) | | h+2=4/1/2 | | 3+ln(8x)=21-2ln(x) | | (X+3)(X-5)=16 | | 10y=14x-40 | | e^6x-7e^3x+6=0 | | (x^1/2)^-2 | | n(0.2+0.5)=3.5 | | 3(0.33+c)=1.06 | | x^2-4x-471=0 | | 4u-1=1-2u | | 5x+2x+6=90 | | -0.4x^2+80x-1600=0 | | x^2-4x-2=y | | x^2-4x-y-2=0 | | -7a+.67(12a+15)-10= | | 8(x+5)+19=267 | | 6/5=x+7/15 | | 6-.2(20a-5)+3a= | | 30x^2+6x-24=0 | | (-9a+6x/2a)+(2a-7x/6a)+2 |

Equations solver categories