b^2-3b=7

Simple and best practice solution for b^2-3b=7 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 b^2-3b=7 equation:


Simplifying
b2 + -3b = 7

Reorder the terms:
-3b + b2 = 7

Solving
-3b + b2 = 7

Solving for variable 'b'.

Reorder the terms:
-7 + -3b + b2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -3b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3b + 7 + b2 = 0 + 7

Reorder the terms:
-7 + 7 + -3b + b2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3b + b2 = 0 + 7
-3b + b2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3b + b2 = 7

The b term is -3b.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3b + 2.25 + b2 = 7 + 2.25

Reorder the terms:
2.25 + -3b + b2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + -3b + b2 = 9.25

Factor a perfect square on the left side:
(b + -1.5)(b + -1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(b + -1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

b + -1.5 = 3.041381265 Simplifying b + -1.5 = 3.041381265 Reorder the terms: -1.5 + b = 3.041381265 Solving -1.5 + b = 3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = 3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 3.041381265 + 1.5 b = 3.041381265 + 1.5 Combine like terms: 3.041381265 + 1.5 = 4.541381265 b = 4.541381265 Simplifying b = 4.541381265

Subproblem 2

b + -1.5 = -3.041381265 Simplifying b + -1.5 = -3.041381265 Reorder the terms: -1.5 + b = -3.041381265 Solving -1.5 + b = -3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = -3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -3.041381265 + 1.5 b = -3.041381265 + 1.5 Combine like terms: -3.041381265 + 1.5 = -1.541381265 b = -1.541381265 Simplifying b = -1.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. b = {4.541381265, -1.541381265}

See similar equations:

| t^2-8t+4=0 | | x^2+12x-7=0 | | 7+x=18 | | -4x+5y(3y+5)=-3 | | g^2-3g=40 | | 0.4(x-2)=x+4 | | 5v^2=19v+4 | | ln(x+5)=ln(x-1)-ln(x+1) | | 4a+24=10a-6a+24 | | 7x=2x^2-4 | | ln(5x)=0 | | 5w^2+2=-7w | | 4(-6+8x)=256 | | 11z+2+19z-2=180 | | 104=2(x+3)(x-1) | | 3v^2=2v+5 | | 3x-3x+9=2 | | 12g-5=15g+7 | | i=(500)(0.14)(2) | | 2b-(1-b)=11-6 | | 2x-2x+5=5 | | 5y^2+7y=2 | | X*X-14=x*5 | | 2t-15=-5(6-t) | | -20v=4v^2+25 | | 70=(x+2)(x)2 | | p=2(16)+2(79) | | 7z+4=8z-5 | | 3w^2=9w | | 3s^2-13s+12=0 | | 6x^2+2x+1=0 | | x-1=20-2x |

Equations solver categories