4x^2+10x-2=0

Simple and best practice solution for 4x^2+10x-2=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 4x^2+10x-2=0 equation: 


Simplifying
4x2 + 10x + -2 = 0

Reorder the terms:
-2 + 10x + 4x2 = 0

Solving
-2 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + 5x + 2x2 = 0

Solving
-1 + 5x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.5x + x2 = 0 + 0.5
2.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.5x + x2 = 0.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.5 + 1.5625

Combine like terms: 0.5 + 1.5625 = 2.0625
1.5625 + 2.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.436140662 and -1.436140662.


Subproblem 1
x + 1.25 = 1.436140662

Simplifying
x + 1.25 = 1.436140662

Reorder the terms:
1.25 + x = 1.436140662

Solving
1.25 + x = 1.436140662

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.436140662 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.436140662 + -1.25
x = 1.436140662 + -1.25

Combine like terms: 1.436140662 + -1.25 = 0.186140662
x = 0.186140662

Simplifying
x = 0.186140662


Subproblem 2
x + 1.25 = -1.436140662

Simplifying
x + 1.25 = -1.436140662

Reorder the terms:
1.25 + x = -1.436140662

Solving
1.25 + x = -1.436140662

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.436140662 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.436140662 + -1.25
x = -1.436140662 + -1.25

Combine like terms: -1.436140662 + -1.25 = -2.686140662
x = -2.686140662

Simplifying
x = -2.686140662


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.186140662, -2.686140662}
Solution
x = {0.186140662, -2.686140662}

See similar equations:

| 19x-7=1+15x | | v-8=-525 | | -.5(-6+12x)= | | 65(5-4g)=-18 | | -4+8=18 | | -3y=64-37 | | 3(x+3)+2(3+x)=180 | | a=rt+r | | 6x-4+72=18+11x | | 13-4=1-x | | 9(x+3)+2(x+3)=6x-6 | | -32+7n=200 | | x+7-11-6=24+1+9 | | (X-1)2= | | -(-5+10x)= | | x+7-11-6+5=24+1+9 | | x+7-11+6+5=24+1+9 | | 25x-25x=-7 | | 6x-8=-7 | | -3p=8p-132 | | 36.6=4a | | 7x-4=5x-20 | | -1.8=4.6-0.4s | | 6t-15=-11t | | 10+x/3=20 | | 8x^2-5x-28=0 | | 5.5/11=x/5 | | 98-3x=42x+18 | | log(x+3)+log(x-5)=2log(x-6) | | 4(v+w+5)= | | -m/5=-2/5 | | 11+x+5x=48 |

Equations solver categories