4x^2-2x-10=0

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


Simplifying
4x2 + -2x + -10 = 0

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

Solving
-10 + -2x + 4x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
-5 + -1x + 2x2 = 0

Solving
-5 + -1x + 2x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + -0.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.600781059 and -1.600781059.


Subproblem 1
x + -0.25 = 1.600781059

Simplifying
x + -0.25 = 1.600781059

Reorder the terms:
-0.25 + x = 1.600781059

Solving
-0.25 + x = 1.600781059

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 1.600781059 + 0.25
x = 1.600781059 + 0.25

Combine like terms: 1.600781059 + 0.25 = 1.850781059
x = 1.850781059

Simplifying
x = 1.850781059


Subproblem 2
x + -0.25 = -1.600781059

Simplifying
x + -0.25 = -1.600781059

Reorder the terms:
-0.25 + x = -1.600781059

Solving
-0.25 + x = -1.600781059

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -1.600781059 + 0.25
x = -1.600781059 + 0.25

Combine like terms: -1.600781059 + 0.25 = -1.350781059
x = -1.350781059

Simplifying
x = -1.350781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.850781059, -1.350781059}
Solution
x = {1.850781059, -1.350781059}

See similar equations:

| 2y=-6+3x | | n/6+2=-8 | | 4x^2-24x+20=-15 | | 4a^2-36a+32=0 | | -11y+4=15 | | 2x^2-8x=24 | | 3.5-20=2.4x+13 | | 4x+3(x+2)=1 | | 3x^4-25x^2-20=0 | | 2/3n+4=-26 | | 5/7+3x/4=2 | | 17+2x=63 | | 3*10*x=v | | W/2+3=10 | | -9t+12=-25 | | 3x/4+1=7 | | 42x^2-54x+1=0 | | x-y=3recta | | (w+3)/5-4=6 | | 9+4x=74-x | | 1.3t+10.9=6.2 | | -x+y-3=0 | | 1/3x-6=9+2/3x | | a/3+4=12 | | 2x+7=2x-9 | | (3x-17)+98=180 | | x=9-3y/4 | | 33a+10=28a-5 | | 17+2x=31-5 | | 9-3y/4=x | | 4-9c+3c=58 | | 14u=2/3 |

Equations solver categories