7a-a^2=-28

Simple and best practice solution for 7a-a^2=-28 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 7a-a^2=-28 equation:


Simplifying
7a + -1a2 = -28

Solving
7a + -1a2 = -28

Solving for variable 'a'.

Reorder the terms:
28 + 7a + -1a2 = -28 + 28

Combine like terms: -28 + 28 = 0
28 + 7a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-28 + -7a + a2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -7a + 28 + a2 = 0 + 28

Reorder the terms:
-28 + 28 + -7a + a2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -7a + a2 = 0 + 28
-7a + a2 = 0 + 28

Combine like terms: 0 + 28 = 28
-7a + a2 = 28

The a term is -7a.  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.
-7a + 12.25 + a2 = 28 + 12.25

Reorder the terms:
12.25 + -7a + a2 = 28 + 12.25

Combine like terms: 28 + 12.25 = 40.25
12.25 + -7a + a2 = 40.25

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

Calculate the square root of the right side: 6.34428877

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

Subproblem 1

a + -3.5 = 6.34428877 Simplifying a + -3.5 = 6.34428877 Reorder the terms: -3.5 + a = 6.34428877 Solving -3.5 + a = 6.34428877 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 6.34428877 + 3.5 a = 6.34428877 + 3.5 Combine like terms: 6.34428877 + 3.5 = 9.84428877 a = 9.84428877 Simplifying a = 9.84428877

Subproblem 2

a + -3.5 = -6.34428877 Simplifying a + -3.5 = -6.34428877 Reorder the terms: -3.5 + a = -6.34428877 Solving -3.5 + a = -6.34428877 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -6.34428877 + 3.5 a = -6.34428877 + 3.5 Combine like terms: -6.34428877 + 3.5 = -2.84428877 a = -2.84428877 Simplifying a = -2.84428877

Solution

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

See similar equations:

| T/9-9=5 | | -y+5x=6-2y | | x=3y-3y | | 2x=(999/8) | | X*3/-4=-6 | | 5x-y=6-2y | | T=36x+60 | | 3x-3+4x+5+2x+16=180 | | 14-40/-2 | | 3[x-4(x-2)]-6=-4x-7 | | (-4)3/4-(-2) | | 7x+5=2x+18+3x+11 | | C=5/9(98-32) | | A=2(pi)(r)(p)+(pi)(r^2) | | 8(6-3r)=120 | | 1/3p=7=12-2/3p | | U-2/3=u/5 | | x-(4x-2)=8-5x | | 16(8)=(10+x)x | | x^2-5x=2x | | 17=p+5+p | | y=0.008x^2-.04x+75 | | a+9=2 | | 7k/7÷3=21 | | 2e+3e+10e=225 | | 1/4*2/4 | | 2-2=r+54-2r | | q-(-2)=12 | | y-0= | | a/-3=10 | | -2r+5=2-2r | | 21-16+l=14 |

Equations solver categories