x^2+7x-28=0

Simple and best practice solution for x^2+7x-28=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 x^2+7x-28=0 equation:


Simplifying
x2 + 7x + -28 = 0

Reorder the terms:
-28 + 7x + x2 = 0

Solving
-28 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 7x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 7x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 7x + x2 = 0 + 28
7x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
7x + x2 = 28

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 28 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 28 + 12.25

Combine like terms: 28 + 12.25 = 40.25
12.25 + 7x + x2 = 40.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + 3.5 = 6.34428877

Simplifying
x + 3.5 = 6.34428877

Reorder the terms:
3.5 + x = 6.34428877

Solving
3.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 6.34428877 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.34428877 + -3.5
x = 6.34428877 + -3.5

Combine like terms: 6.34428877 + -3.5 = 2.84428877
x = 2.84428877

Simplifying
x = 2.84428877


Subproblem 2
x + 3.5 = -6.34428877

Simplifying
x + 3.5 = -6.34428877

Reorder the terms:
3.5 + x = -6.34428877

Solving
3.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -6.34428877 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.34428877 + -3.5
x = -6.34428877 + -3.5

Combine like terms: -6.34428877 + -3.5 = -9.84428877
x = -9.84428877

Simplifying
x = -9.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.84428877, -9.84428877}

See similar equations:

| 1+9x=1+x | | (3y+6)(y-7z-2)= | | 7+4(d-3)=23 | | 12x+48=16x | | -5(5y-10)+4(2y+6)= | | 10+x-x-4=3+x+1 | | 6f+2=3f+20 | | 10+x-x-4=3+x+7 | | x+2x-3+1=x+x+7 | | 35=7x-6(2x-15) | | 5/4+m/4=22 | | -(5+7i)(5+7i)= | | 2(2x-3)=2 | | 6.5x+8y=3561 | | (x-1)(x+4)=(x-5) | | -2(b-4)=4 | | 2(13-x)=x-1 | | 3(2x-4)=7x+8 | | 122=11x+1 | | (x-1)+(x+4)=(x-5) | | -4=14x | | 75=2x+1 | | log[5](x-1)-log[5](x+4)=log[5](x-5) | | 10x-4=21 | | 5y+3y-5y-3=18 | | 654+3322= | | 2x-50=40 | | 4a+-3(a-2)=2(3a-2) | | (x^2)-17x+52=0 | | long[5](x-1)-log[5](x+4)=log[5](x-5) | | 4x=-100 | | 8u+3-2=w |

Equations solver categories