4x^2+2x-34=0

Simple and best practice solution for 4x^2+2x-34=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-34=0 equation: 


Simplifying
4x2 + 2x + -34 = 0

Reorder the terms:
-34 + 2x + 4x2 = 0

Solving
-34 + 2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
-17 + x + 2x2 = 0

Solving
-17 + x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 0.5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 0.5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 0.5x + x2 = 0 + 8.5
0.5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
0.5x + x2 = 8.5

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

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = 8.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 8.5 + 0.25

Combine like terms: 8.5 + 0.25 = 8.75
0.25 + 0.5x + x2 = 8.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.958039892 and -2.958039892.


Subproblem 1
x + 0.5 = 2.958039892

Simplifying
x + 0.5 = 2.958039892

Reorder the terms:
0.5 + x = 2.958039892

Solving
0.5 + x = 2.958039892

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.958039892 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.958039892 + -0.5
x = 2.958039892 + -0.5

Combine like terms: 2.958039892 + -0.5 = 2.458039892
x = 2.458039892

Simplifying
x = 2.458039892


Subproblem 2
x + 0.5 = -2.958039892

Simplifying
x + 0.5 = -2.958039892

Reorder the terms:
0.5 + x = -2.958039892

Solving
0.5 + x = -2.958039892

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.958039892 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.958039892 + -0.5
x = -2.958039892 + -0.5

Combine like terms: -2.958039892 + -0.5 = -3.458039892
x = -3.458039892

Simplifying
x = -3.458039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.458039892, -3.458039892}
Solution
x = {2.458039892, -3.458039892}

See similar equations:

| 4x-36=y | | 10(c-b)-40=20a | | 6+2x(5-1)= | | 3x+m=5 | | -25-4x=-6x+31 | | 12+4t=8 | | 5a-7b=4forb | | -7(a+5)=-84 | | 8-3+1b=b-9 | | 4d-9=3 | | -13-11x=-9x+19 | | (-3x+6)=(2x+3)-15 | | 3x^2-4x+2=O | | b=116 | | x(x-8)=-20 | | -5x+12-7x=2+3x-14x+10 | | -8(1-3k)=184 | | 2z+3y=2d | | -8y-5x=16 | | 2secX=18 | | -3x^4=144 | | 52+6*3-48= | | -20+7x=-4x-6x | | x-81=12x+128 | | -92=-4(-3n+2) | | 3(2x-1)+4y=10x | | 78-(4x+5)=4(x+7)+x | | (2.5)(5)=m-17+4 | | y=x^5+1 | | -5x^3=120 | | 70+x=5(x+2) | | 5y-4x=2x+10 |

Equations solver categories