a^2-25a+16=

Simple and best practice solution for a^2-25a+16= 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 a^2-25a+16= equation:


Simplifying
a2 + -25a + 16 = 0

Reorder the terms:
16 + -25a + a2 = 0

Solving
16 + -25a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -25a + -16 + a2 = 0 + -16

Reorder the terms:
16 + -16 + -25a + a2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -25a + a2 = 0 + -16
-25a + a2 = 0 + -16

Combine like terms: 0 + -16 = -16
-25a + a2 = -16

The a term is -25a.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25a + 156.25 + a2 = -16 + 156.25

Reorder the terms:
156.25 + -25a + a2 = -16 + 156.25

Combine like terms: -16 + 156.25 = 140.25
156.25 + -25a + a2 = 140.25

Factor a perfect square on the left side:
(a + -12.5)(a + -12.5) = 140.25

Calculate the square root of the right side: 11.842719282

Break this problem into two subproblems by setting 
(a + -12.5) equal to 11.842719282 and -11.842719282.

Subproblem 1

a + -12.5 = 11.842719282 Simplifying a + -12.5 = 11.842719282 Reorder the terms: -12.5 + a = 11.842719282 Solving -12.5 + a = 11.842719282 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + a = 11.842719282 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = 11.842719282 + 12.5 a = 11.842719282 + 12.5 Combine like terms: 11.842719282 + 12.5 = 24.342719282 a = 24.342719282 Simplifying a = 24.342719282

Subproblem 2

a + -12.5 = -11.842719282 Simplifying a + -12.5 = -11.842719282 Reorder the terms: -12.5 + a = -11.842719282 Solving -12.5 + a = -11.842719282 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + a = -11.842719282 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = -11.842719282 + 12.5 a = -11.842719282 + 12.5 Combine like terms: -11.842719282 + 12.5 = 0.657280718 a = 0.657280718 Simplifying a = 0.657280718

Solution

The solution to the problem is based on the solutions from the subproblems. a = {24.342719282, 0.657280718}

See similar equations:

| k^2+5k+6= | | 5(x+4)=2+3 | | 4x-12=-24 | | 7x+21=-28 | | x^2+x^2=36 | | -110+6x=74 | | 4x^2+2x-17=0 | | 4x^2-3x-1= | | 3n^2+12n-288=0 | | 5x=3y-2x+4y | | 0=-16t^2+14+6 | | 5x-3x+6=0 | | 7y=2y+20 | | 7p-17=9+31p | | 4x-28=32 | | 20x^4-14x^2-12x=0 | | 2a-1+5a=9+4a+27 | | 3n^2=6n | | x+18= | | 5t^2-9t+18=0 | | 3x+12=96 | | 14.95+0.13x=-15.00+0.39x | | 2d^2-21d-65=0 | | 9-3x=5x+6 | | -3(3r+3)+4= | | 2(x-4)+6x= | | 14.95+0.13x=50.00 | | 2b-(5+4b)= | | x(x)-2x-8=0 | | -15.00+0.39x=50.00 | | y=-2x^2+2x+1 | | 4(x+4)+3= |

Equations solver categories