506.25b^2-600b+100=0

Simple and best practice solution for 506.25b^2-600b+100=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 506.25b^2-600b+100=0 equation:


Simplifying
506.25b2 + -600b + 100 = 0

Reorder the terms:
100 + -600b + 506.25b2 = 0

Solving
100 + -600b + 506.25b2 = 0

Solving for variable 'b'.

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

Divide each side by '506.25'.
0.1975308642 + -1.185185185b + b2 = 0

Move the constant term to the right:

Add '-0.1975308642' to each side of the equation.
0.1975308642 + -1.185185185b + -0.1975308642 + b2 = 0 + -0.1975308642

Reorder the terms:
0.1975308642 + -0.1975308642 + -1.185185185b + b2 = 0 + -0.1975308642

Combine like terms: 0.1975308642 + -0.1975308642 = 0.0000000000
0.0000000000 + -1.185185185b + b2 = 0 + -0.1975308642
-1.185185185b + b2 = 0 + -0.1975308642

Combine like terms: 0 + -0.1975308642 = -0.1975308642
-1.185185185b + b2 = -0.1975308642

The b term is -1.185185185b.  Take half its coefficient (-0.5925925925).
Square it (0.3511659807) and add it to both sides.

Add '0.3511659807' to each side of the equation.
-1.185185185b + 0.3511659807 + b2 = -0.1975308642 + 0.3511659807

Reorder the terms:
0.3511659807 + -1.185185185b + b2 = -0.1975308642 + 0.3511659807

Combine like terms: -0.1975308642 + 0.3511659807 = 0.1536351165
0.3511659807 + -1.185185185b + b2 = 0.1536351165

Factor a perfect square on the left side:
(b + -0.5925925925)(b + -0.5925925925) = 0.1536351165

Calculate the square root of the right side: 0.391963157

Break this problem into two subproblems by setting 
(b + -0.5925925925) equal to 0.391963157 and -0.391963157.

Subproblem 1

b + -0.5925925925 = 0.391963157 Simplifying b + -0.5925925925 = 0.391963157 Reorder the terms: -0.5925925925 + b = 0.391963157 Solving -0.5925925925 + b = 0.391963157 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5925925925' to each side of the equation. -0.5925925925 + 0.5925925925 + b = 0.391963157 + 0.5925925925 Combine like terms: -0.5925925925 + 0.5925925925 = 0.0000000000 0.0000000000 + b = 0.391963157 + 0.5925925925 b = 0.391963157 + 0.5925925925 Combine like terms: 0.391963157 + 0.5925925925 = 0.9845557495 b = 0.9845557495 Simplifying b = 0.9845557495

Subproblem 2

b + -0.5925925925 = -0.391963157 Simplifying b + -0.5925925925 = -0.391963157 Reorder the terms: -0.5925925925 + b = -0.391963157 Solving -0.5925925925 + b = -0.391963157 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5925925925' to each side of the equation. -0.5925925925 + 0.5925925925 + b = -0.391963157 + 0.5925925925 Combine like terms: -0.5925925925 + 0.5925925925 = 0.0000000000 0.0000000000 + b = -0.391963157 + 0.5925925925 b = -0.391963157 + 0.5925925925 Combine like terms: -0.391963157 + 0.5925925925 = 0.2006294355 b = 0.2006294355 Simplifying b = 0.2006294355

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.9845557495, 0.2006294355}

See similar equations:

| b^2-1.185b+0.197=0 | | 3y=11y-10 | | 10v^3+36v^2-70v=0 | | 5f+2=3f+5 | | 0.5x+3=-1 | | 10c^2-27c+5=0 | | 20n+3(4n-7)= | | 5(x+2)=2x-5 | | 7/12-2/6 | | 2(x+6)+4= | | 5(x+3)+4=3x+17 | | f(x)=115x+49 | | (8n+20)= | | 8c^3+18c^2-56c=0 | | 2(4x-y+10)= | | 9(7+6t)= | | 7(3n+5)= | | 72+68+82+X=73 | | 15(k-2)= | | 4x+11=-85-5x | | x^6+2x^4-3x^3=0 | | 10(y+4)= | | -5(8-3k)= | | (12x^7-6x^5)/2x^3 | | 30t-4(t+3)= | | 60000=2.5x-x | | 7+11x=-53+x | | 700/x=63 | | -(57-3t)= | | 20-(y+7)= | | X/4.08=7.2=5.14 | | 2x^2+3+8=33(2x) |

Equations solver categories