2x^2+11x+7=0

Simple and best practice solution for 2x^2+11x+7=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 2x^2+11x+7=0 equation: 


Simplifying
2x2 + 11x + 7 = 0

Reorder the terms:
7 + 11x + 2x2 = 0

Solving
7 + 11x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
3.5 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 5.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 5.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 5.5x + x2 = 0 + -3.5
5.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
5.5x + x2 = -3.5

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -3.5 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -3.5 + 7.5625

Combine like terms: -3.5 + 7.5625 = 4.0625
7.5625 + 5.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 2.75) equal to 2.015564437 and -2.015564437.


Subproblem 1
x + 2.75 = 2.015564437

Simplifying
x + 2.75 = 2.015564437

Reorder the terms:
2.75 + x = 2.015564437

Solving
2.75 + x = 2.015564437

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 2.015564437 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 2.015564437 + -2.75
x = 2.015564437 + -2.75

Combine like terms: 2.015564437 + -2.75 = -0.734435563
x = -0.734435563

Simplifying
x = -0.734435563


Subproblem 2
x + 2.75 = -2.015564437

Simplifying
x + 2.75 = -2.015564437

Reorder the terms:
2.75 + x = -2.015564437

Solving
2.75 + x = -2.015564437

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -2.015564437 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -2.015564437 + -2.75
x = -2.015564437 + -2.75

Combine like terms: -2.015564437 + -2.75 = -4.765564437
x = -4.765564437

Simplifying
x = -4.765564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.734435563, -4.765564437}

See similar equations:

| 5(4.6+0.4y)-2y=23 | | 7n+2n-0.06=0.03+6n+0.10 | | 4+8x+2+(99-x)= | | 38=.4x | | 4+8x+2+(99+x)= | | 8x-20=5x-12 | | x+2=-(4x+4) | | 4+8x+2(99+x)= | | -12+x=x+27 | | -4(-7+5x)=-132 | | p+0.06p=201.4 | | 6x+5=3x+8 | | 50+12x-1.5x^2=0 | | 7(-5-4x)=-119 | | 5x-2(4)=23 | | 2(-4.6+0.4y)=-6 | | 7x+1=3x-2 | | -3(x-3)=x | | 7(1+4x)=7 | | 2x-3-5x+2=14 | | -3(x+9)=x | | 8x-9x=2-x-15 | | -3x+7=3x-53 | | 4z+12=2z+4 | | 7z-13-3z+5=0 | | 16x-7=5+14x | | 4+x*2=7+x | | -3(2x+7)=-27 | | 4e^2x=20 | | 3x(-7)=21 | | 4-6w= | | 8(t-2)+7t=5(3t+3)-10 |

Equations solver categories