2(x^2)+2x=6

Simple and best practice solution for 2(x^2)+2x=6 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 2(x^2)+2x=6 equation: 


Simplifying
2(x2) + 2x = 6

Reorder the terms:
2x + 2x2 = 6

Solving
2x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 2x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + x + x2 = 0

Solving
-3 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + x + x2 = 0 + 3

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

Combine like terms: 0 + 3 = 3
x + x2 = 3

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.
x + 0.25 + x2 = 3 + 0.25

Reorder the terms:
0.25 + x + x2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + x + x2 = 3.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 0.5 = 1.802775638

Simplifying
x + 0.5 = 1.802775638

Reorder the terms:
0.5 + x = 1.802775638

Solving
0.5 + x = 1.802775638

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 = 1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.802775638 + -0.5
x = 1.802775638 + -0.5

Combine like terms: 1.802775638 + -0.5 = 1.302775638
x = 1.302775638

Simplifying
x = 1.302775638


Subproblem 2
x + 0.5 = -1.802775638

Simplifying
x + 0.5 = -1.802775638

Reorder the terms:
0.5 + x = -1.802775638

Solving
0.5 + x = -1.802775638

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 = -1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.802775638 + -0.5
x = -1.802775638 + -0.5

Combine like terms: -1.802775638 + -0.5 = -2.302775638
x = -2.302775638

Simplifying
x = -2.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.302775638, -2.302775638}
Solution
x = {1.302775638, -2.302775638}

See similar equations:

| 1/(w+1)=-4-(7/(w-2)) | | -0.80(20)+0.70x=0.40(20+x) | | 78.7+1.3*1.3*0.8= | | 3056890000.00-15000000.00n=3000000000.00 | | -7/((v+1)(v-7))=4+(3/(v-7)) | | 1.3*1.3= | | 4(x^2)+2x=14 | | x-.30=105 | | 12=6*(x/10000)^0.5 | | 4/(v-1)=-6+(5/(v+2)) | | 2z/z+4=3z/2z-5 | | 6+(6/(u-3))=5/(u+1) | | 0=2x^2-4x+13 | | 2z/z+4=3z-2z-5 | | 2.5m+3.6=7.8-9.6m | | (x/x-5)-(5)=5/x-5 | | y-(-6.4)=-28 | | 6x+18=4x+12 | | -3/7-3/2v=3/5 | | -6/7(2x+6)=1/28x-17 | | 6+6/(u+3)=5/(u+1) | | 14/x-3=15-1/x-3 | | 7=-5z+8 | | .625x=-5 | | x+35/x+12=0 | | -3-(5/(u+5))=-5/((u+2)(u+5)) | | -1/5=-1/3v+1/5 | | 0=-2x^2-28x-90 | | .45x+.5(12-x)=.10(-42) | | 3x-22=9 | | 6-(1/(x+1))=4/(x+2) | | -3/2-3/5w=-2/3 |

Equations solver categories