a^2+5a-25=0

Simple and best practice solution for a^2+5a-25=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 a^2+5a-25=0 equation:


Simplifying
a2 + 5a + -25 = 0

Reorder the terms:
-25 + 5a + a2 = 0

Solving
-25 + 5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 5a + 25 + a2 = 0 + 25

Reorder the terms:
-25 + 25 + 5a + a2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 5a + a2 = 0 + 25
5a + a2 = 0 + 25

Combine like terms: 0 + 25 = 25
5a + a2 = 25

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = 25 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + 5a + a2 = 31.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(a + 2.5) equal to 5.590169944 and -5.590169944.

Subproblem 1

a + 2.5 = 5.590169944 Simplifying a + 2.5 = 5.590169944 Reorder the terms: 2.5 + a = 5.590169944 Solving 2.5 + a = 5.590169944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 5.590169944 + -2.5 a = 5.590169944 + -2.5 Combine like terms: 5.590169944 + -2.5 = 3.090169944 a = 3.090169944 Simplifying a = 3.090169944

Subproblem 2

a + 2.5 = -5.590169944 Simplifying a + 2.5 = -5.590169944 Reorder the terms: 2.5 + a = -5.590169944 Solving 2.5 + a = -5.590169944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -5.590169944 + -2.5 a = -5.590169944 + -2.5 Combine like terms: -5.590169944 + -2.5 = -8.090169944 a = -8.090169944 Simplifying a = -8.090169944

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.090169944, -8.090169944}

See similar equations:

| -4(-6u+4)-8u=4(u-1)-9 | | ln(3x-13)=4 | | 1/7n=12 | | x+-12=-3 | | 4=10-3q | | -3x-2(6x-5)=-155 | | 5+3t+3t+2+10t= | | m^2(12m+4m)=5m | | -6(v-9)=3v+36 | | (4m/7n^2)^2 | | 24a+22=-4(1-6a) | | 1-10=81 | | 7+x=105 | | 4x-3y-4x-2y= | | 4v+34=6(v+7) | | (4x-8)+34+76-x=180 | | X-4/5=7/9 | | 100-7/r=44 | | 5z^2-17z=14 | | 44-x=9x-76 | | 2x^2-8x-102=0 | | 4(3a-2)=8d-5 | | 5z-17z=14 | | 6t-t-6=4t-3 | | 6r^2-10r=24 | | 3ax-4x+1-7+3x-4ax= | | 3b+5b+10b=72 | | 112y+16=24y-32 | | 1=6(1-1p) | | 3.5x=-14 | | x+40=580 | | 100-7r=0 |

Equations solver categories