a^2+5a-45=

Simple and best practice solution for a^2+5a-45= 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-45= equation:


Simplifying
a2 + 5a + -45 = 0

Reorder the terms:
-45 + 5a + a2 = 0

Solving
-45 + 5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 5a + 45 + a2 = 0 + 45

Reorder the terms:
-45 + 45 + 5a + a2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 5a + a2 = 0 + 45
5a + a2 = 0 + 45

Combine like terms: 0 + 45 = 45
5a + a2 = 45

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 = 45 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 45 + 6.25

Combine like terms: 45 + 6.25 = 51.25
6.25 + 5a + a2 = 51.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(a + 2.5) equal to 7.158910532 and -7.158910532.

Subproblem 1

a + 2.5 = 7.158910532 Simplifying a + 2.5 = 7.158910532 Reorder the terms: 2.5 + a = 7.158910532 Solving 2.5 + a = 7.158910532 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 = 7.158910532 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 7.158910532 + -2.5 a = 7.158910532 + -2.5 Combine like terms: 7.158910532 + -2.5 = 4.658910532 a = 4.658910532 Simplifying a = 4.658910532

Subproblem 2

a + 2.5 = -7.158910532 Simplifying a + 2.5 = -7.158910532 Reorder the terms: 2.5 + a = -7.158910532 Solving 2.5 + a = -7.158910532 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 = -7.158910532 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -7.158910532 + -2.5 a = -7.158910532 + -2.5 Combine like terms: -7.158910532 + -2.5 = -9.658910532 a = -9.658910532 Simplifying a = -9.658910532

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.658910532, -9.658910532}

See similar equations:

| 1/2=20x-12 | | 7+7x+8= | | 2w+2(4w-6)=548 | | y=11(-2) | | 7-2(5n-8m)= | | 7+5x=9x | | -6x-7c+3+c-2x+8= | | 13+13=24 | | (N)2-12=-14 | | 15-9x/-4 | | 8x+9y+3x+9y= | | 35=2b+5 | | (2x^2-5x^3)-(8x^2-8x^3)=0 | | 63=-3(1-2x)-6(1-2x) | | (x^3-2x^2+4x-8)=y | | 4x+3y+6x+9y= | | 6r=5(2r-4) | | 4x^2-31x+65=0 | | 5x^2+7x-5x+4x^2= | | 6x+1=2x+49 | | 5y+2g-3y+8y= | | n2-n/5=0 | | 2/7m=3/14 | | 6x-3=10x+12 | | -8(7-9)+3(3-6)=y | | 3(y+3)+5=4(y+1)+5 | | -12x+5b+3+10b-10x+11= | | m=-9/1 | | -16=3(m+4)-4(7-5m) | | (x+5)(x-5)=x^2+2x-3 | | 31/2X5 | | -7x-2+3x-3=y |

Equations solver categories