5a^2-6a=1

Simple and best practice solution for 5a^2-6a=1 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^2-6a=1 equation:


Simplifying
5a2 + -6a = 1

Reorder the terms:
-6a + 5a2 = 1

Solving
-6a + 5a2 = 1

Solving for variable 'a'.

Reorder the terms:
-1 + -6a + 5a2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -6a + 5a2 = 0

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

Divide each side by '5'.
-0.2 + -1.2a + a2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.2a + 0.2 + a2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.2a + a2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.2a + a2 = 0 + 0.2
-1.2a + a2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-1.2a + a2 = 0.2

The a term is -1.2a.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2a + 0.36 + a2 = 0.2 + 0.36

Reorder the terms:
0.36 + -1.2a + a2 = 0.2 + 0.36

Combine like terms: 0.2 + 0.36 = 0.56
0.36 + -1.2a + a2 = 0.56

Factor a perfect square on the left side:
(a + -0.6)(a + -0.6) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(a + -0.6) equal to 0.748331477 and -0.748331477.

Subproblem 1

a + -0.6 = 0.748331477 Simplifying a + -0.6 = 0.748331477 Reorder the terms: -0.6 + a = 0.748331477 Solving -0.6 + a = 0.748331477 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + a = 0.748331477 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + a = 0.748331477 + 0.6 a = 0.748331477 + 0.6 Combine like terms: 0.748331477 + 0.6 = 1.348331477 a = 1.348331477 Simplifying a = 1.348331477

Subproblem 2

a + -0.6 = -0.748331477 Simplifying a + -0.6 = -0.748331477 Reorder the terms: -0.6 + a = -0.748331477 Solving -0.6 + a = -0.748331477 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + a = -0.748331477 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + a = -0.748331477 + 0.6 a = -0.748331477 + 0.6 Combine like terms: -0.748331477 + 0.6 = -0.148331477 a = -0.148331477 Simplifying a = -0.148331477

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.348331477, -0.148331477}

See similar equations:

| (10b-6)-3(3b+2)=-3 | | x^2-8x+15.75=0 | | y=0(0)-7 | | (4y+9)(4y+9)=64y^3+432y^2+972y+729 | | 5c+6=2-y | | 5x+6x+3+8=3x+5+7x | | 16+-8-9= | | z^2-8z-20= | | 3(Q-6)=2(2Q+7)+10 | | 25+-15-12= | | 15x^2+5x-20= | | y=18(0)+0 | | 9y^2+21y+6= | | 2x+3x=30-z | | y=-7(0)+4 | | 3x^2-4y=20 | | 3x^2-4y=20 | | 5(t-3)+7t=4(3t+3)-10 | | 2x^2+5y^2=30 | | -2(5s-6)-12=-2(7s+2)-3 | | 0.25(x-2)=8 | | 5(y+1)+3=3y-20 | | 10+b+10=35 | | 5+t-4=16+9 | | M+4+9=14-9 | | 0.25(t+10)=5 | | 10d+8=5d+33 | | 7xy*7xy^2*7x^2y= | | 2(x-9)=-8.8 | | 2(x-9)=8.8 | | 6(a+7)=63 | | 5x-3+7x=4x+4-6x |

Equations solver categories