3x^2+5x-1=-2

Simple and best practice solution for 3x^2+5x-1=-2 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+5x-1=-2 equation: 


Simplifying
3x2 + 5x + -1 = -2

Reorder the terms:
-1 + 5x + 3x2 = -2

Solving
-1 + 5x + 3x2 = -2

Solving for variable 'x'.

Reorder the terms:
-1 + 2 + 5x + 3x2 = -2 + 2

Combine like terms: -1 + 2 = 1
1 + 5x + 3x2 = -2 + 2

Combine like terms: -2 + 2 = 0
1 + 5x + 3x2 = 0

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

Divide each side by '3'.
0.3333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.666666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.666666667x + x2 = 0 + -0.3333333333
1.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.666666667x + x2 = -0.3333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -0.3333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -0.3333333333 + 0.6944444447

Combine like terms: -0.3333333333 + 0.6944444447 = 0.3611111114
0.6944444447 + 1.666666667x + x2 = 0.3611111114

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 0.3611111114

Calculate the square root of the right side: 0.600925213

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 0.600925213 and -0.600925213.


Subproblem 1
x + 0.8333333335 = 0.600925213

Simplifying
x + 0.8333333335 = 0.600925213

Reorder the terms:
0.8333333335 + x = 0.600925213

Solving
0.8333333335 + x = 0.600925213

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 0.600925213 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 0.600925213 + -0.8333333335
x = 0.600925213 + -0.8333333335

Combine like terms: 0.600925213 + -0.8333333335 = -0.2324081205
x = -0.2324081205

Simplifying
x = -0.2324081205


Subproblem 2
x + 0.8333333335 = -0.600925213

Simplifying
x + 0.8333333335 = -0.600925213

Reorder the terms:
0.8333333335 + x = -0.600925213

Solving
0.8333333335 + x = -0.600925213

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -0.600925213 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -0.600925213 + -0.8333333335
x = -0.600925213 + -0.8333333335

Combine like terms: -0.600925213 + -0.8333333335 = -1.4342585465
x = -1.4342585465

Simplifying
x = -1.4342585465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.2324081205, -1.4342585465}

See similar equations:

| 7n-12-3n=8(3+2n) | | -8(2x-6)=128 | | 1/2(14)(10) | | 6x-4y=68 | | 23=1.5x | | 6m+2=3m-4 | | y=7x^2+28x+19 | | 2x-14=7-1x | | 45k+18+28-40k= | | 102b+b^2=3 | | -8(-7x-2)=-152 | | 16k^2-114n=-14 | | 0=6x^4-3x^2-1 | | 15-8=-9 | | x(-0.01x+0.05)=0 | | 2y+2x+z=6 | | 9x-10=5x+23 | | 180=40+x+y | | 6ln(8x)=10 | | 30+5h=4+12h | | -234=-7(1-8x)-3 | | 6/5=-5/6k | | 0.5+125=180 | | 0.5+125=100 | | 5-x/6=-13 | | -95=5(3n+5) | | 20X+10Y=90 | | 1/3(6x-3)=11-x | | -3(4-5x)=-12 | | -5w+4(2+2a)=-1 | | 2m=112 | | -3y+x=1 |

Equations solver categories