3x^2+5x-1=4

Simple and best practice solution for 3x^2+5x-1=4 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=4 equation: 


Simplifying
3x2 + 5x + -1 = 4

Reorder the terms:
-1 + 5x + 3x2 = 4

Solving
-1 + 5x + 3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-1 + -4 + 5x + 3x2 = 4 + -4

Combine like terms: -1 + -4 = -5
-5 + 5x + 3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-5 + 5x + 3x2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 1.666666667
1.666666667x + x2 = 0 + 1.666666667

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

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 = 1.666666667 + 0.6944444447

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

Combine like terms: 1.666666667 + 0.6944444447 = 2.3611111117
0.6944444447 + 1.666666667x + x2 = 2.3611111117

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 2.3611111117

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.536590743 and -1.536590743.


Subproblem 1
x + 0.8333333335 = 1.536590743

Simplifying
x + 0.8333333335 = 1.536590743

Reorder the terms:
0.8333333335 + x = 1.536590743

Solving
0.8333333335 + x = 1.536590743

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 = 1.536590743 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.536590743 + -0.8333333335
x = 1.536590743 + -0.8333333335

Combine like terms: 1.536590743 + -0.8333333335 = 0.7032574095
x = 0.7032574095

Simplifying
x = 0.7032574095


Subproblem 2
x + 0.8333333335 = -1.536590743

Simplifying
x + 0.8333333335 = -1.536590743

Reorder the terms:
0.8333333335 + x = -1.536590743

Solving
0.8333333335 + x = -1.536590743

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 = -1.536590743 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.536590743 + -0.8333333335
x = -1.536590743 + -0.8333333335

Combine like terms: -1.536590743 + -0.8333333335 = -2.3699240765
x = -2.3699240765

Simplifying
x = -2.3699240765


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7032574095, -2.3699240765}

See similar equations:

| 7s+35=112 | | -3c-1=-9-2c | | 27j-54= | | 1-1/6 | | 25=x-1/6x | | 7h=6h+6 | | 5x+2+3x+6= | | -m+1=-2m+10 | | 51-w=34.5 | | -6(x+5)+3=-7x+8 | | -m+1=-2+10 | | -3-4h=-5h | | 3x+3(13)-15=4x+4(-2)-9 | | 2(-x+5)+2=5(2x-7) | | 2(x-11)=6 | | 3d+8=5d | | 2cosx-sen(2x)=0 | | 224/(2x((8/8x4)) | | 4c=3c-9 | | 5(x-2)=3x-43 | | z/10-3=3 | | 224/(2x(8/8)x4) | | z/-= | | 3-2n(n+4)=0 | | 4b-9b-13-6+16b=1-8+6b | | 3x-2=13-x | | 3.8x-(-1-9.7x)=2.6 | | (3x+2)+x=22 | | (3x+2)x=22 | | 4(2x-3)-2(x+5)= | | =x^2+x-90 | | -7w/6=-49 |

Equations solver categories