(5a^2-3a+9)-(20a^2+11a-6)=0

Simple and best practice solution for (5a^2-3a+9)-(20a^2+11a-6)=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 (5a^2-3a+9)-(20a^2+11a-6)=0 equation:


Simplifying
(5a2 + -3a + 9) + -1(20a2 + 11a + -6) = 0

Reorder the terms:
(9 + -3a + 5a2) + -1(20a2 + 11a + -6) = 0

Remove parenthesis around (9 + -3a + 5a2)
9 + -3a + 5a2 + -1(20a2 + 11a + -6) = 0

Reorder the terms:
9 + -3a + 5a2 + -1(-6 + 11a + 20a2) = 0
9 + -3a + 5a2 + (-6 * -1 + 11a * -1 + 20a2 * -1) = 0
9 + -3a + 5a2 + (6 + -11a + -20a2) = 0

Reorder the terms:
9 + 6 + -3a + -11a + 5a2 + -20a2 = 0

Combine like terms: 9 + 6 = 15
15 + -3a + -11a + 5a2 + -20a2 = 0

Combine like terms: -3a + -11a = -14a
15 + -14a + 5a2 + -20a2 = 0

Combine like terms: 5a2 + -20a2 = -15a2
15 + -14a + -15a2 = 0

Solving
15 + -14a + -15a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-1 + 0.9333333333a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.9333333333a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.9333333333a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.9333333333a + a2 = 0 + 1
0.9333333333a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.9333333333a + a2 = 1

The a term is 0.9333333333a.  Take half its coefficient (0.4666666667).
Square it (0.2177777778) and add it to both sides.

Add '0.2177777778' to each side of the equation.
0.9333333333a + 0.2177777778 + a2 = 1 + 0.2177777778

Reorder the terms:
0.2177777778 + 0.9333333333a + a2 = 1 + 0.2177777778

Combine like terms: 1 + 0.2177777778 = 1.2177777778
0.2177777778 + 0.9333333333a + a2 = 1.2177777778

Factor a perfect square on the left side:
(a + 0.4666666667)(a + 0.4666666667) = 1.2177777778

Calculate the square root of the right side: 1.10352969

Break this problem into two subproblems by setting 
(a + 0.4666666667) equal to 1.10352969 and -1.10352969.

Subproblem 1

a + 0.4666666667 = 1.10352969 Simplifying a + 0.4666666667 = 1.10352969 Reorder the terms: 0.4666666667 + a = 1.10352969 Solving 0.4666666667 + a = 1.10352969 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + a = 1.10352969 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + a = 1.10352969 + -0.4666666667 a = 1.10352969 + -0.4666666667 Combine like terms: 1.10352969 + -0.4666666667 = 0.6368630233 a = 0.6368630233 Simplifying a = 0.6368630233

Subproblem 2

a + 0.4666666667 = -1.10352969 Simplifying a + 0.4666666667 = -1.10352969 Reorder the terms: 0.4666666667 + a = -1.10352969 Solving 0.4666666667 + a = -1.10352969 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + a = -1.10352969 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + a = -1.10352969 + -0.4666666667 a = -1.10352969 + -0.4666666667 Combine like terms: -1.10352969 + -0.4666666667 = -1.5701963567 a = -1.5701963567 Simplifying a = -1.5701963567

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.6368630233, -1.5701963567}

See similar equations:

| 5x+3(4x-6)=0 | | 8y+3(y-6)=6(y+1)-3 | | 12-6x=-5 | | 5y+3(y-5)=5(9+1)-3 | | -3(-8+6x)=132 | | 3m+2n+9m+4n= | | 2(X-8)=-20 | | 8(4b+2)=-240 | | 8-7s+4s=1s+13 | | (620+x)-300=3x | | -5w-7=98 | | (4xy^2+2y)dx+(4x^2y+2x)dy=0 | | -2a+b=9 | | 0.04x+0.08y=100 | | -4(1+5m)=-6m-14 | | r^3-4r^2-16r+64=0 | | 3x^2+11x-26=0 | | 4m+12=56 | | 4n=4+8+5 | | 8x^2+16x+73=7 | | 2(7x+9)=14x+18 | | 0.45n=3.15forn | | 2x^2-16x+a=0 | | 66=2x-20 | | 0.36y=2.16y | | 3x+17=8x-46 | | 0.08(y-4)+0.12y=0.04y-1.4 | | N=4-10 | | 15x-5=13x-15 | | x*3+2=6 | | 0.08(y-4)+0.12y=0.4y-1.4 | | -80=-9n |

Equations solver categories