5a^2-41a+1=7

Simple and best practice solution for 5a^2-41a+1=7 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^2-41a+1=7 equation:


Simplifying
5a2 + -41a + 1 = 7

Reorder the terms:
1 + -41a + 5a2 = 7

Solving
1 + -41a + 5a2 = 7

Solving for variable 'a'.

Reorder the terms:
1 + -7 + -41a + 5a2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + -41a + 5a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + -41a + 5a2 = 0

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

Divide each side by '5'.
-1.2 + -8.2a + a2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -8.2a + 1.2 + a2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -8.2a + a2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -8.2a + a2 = 0 + 1.2
-8.2a + a2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-8.2a + a2 = 1.2

The a term is -8.2a.  Take half its coefficient (-4.1).
Square it (16.81) and add it to both sides.

Add '16.81' to each side of the equation.
-8.2a + 16.81 + a2 = 1.2 + 16.81

Reorder the terms:
16.81 + -8.2a + a2 = 1.2 + 16.81

Combine like terms: 1.2 + 16.81 = 18.01
16.81 + -8.2a + a2 = 18.01

Factor a perfect square on the left side:
(a + -4.1)(a + -4.1) = 18.01

Calculate the square root of the right side: 4.243819035

Break this problem into two subproblems by setting 
(a + -4.1) equal to 4.243819035 and -4.243819035.

Subproblem 1

a + -4.1 = 4.243819035 Simplifying a + -4.1 = 4.243819035 Reorder the terms: -4.1 + a = 4.243819035 Solving -4.1 + a = 4.243819035 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + a = 4.243819035 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + a = 4.243819035 + 4.1 a = 4.243819035 + 4.1 Combine like terms: 4.243819035 + 4.1 = 8.343819035 a = 8.343819035 Simplifying a = 8.343819035

Subproblem 2

a + -4.1 = -4.243819035 Simplifying a + -4.1 = -4.243819035 Reorder the terms: -4.1 + a = -4.243819035 Solving -4.1 + a = -4.243819035 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + a = -4.243819035 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + a = -4.243819035 + 4.1 a = -4.243819035 + 4.1 Combine like terms: -4.243819035 + 4.1 = -0.143819035 a = -0.143819035 Simplifying a = -0.143819035

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.343819035, -0.143819035}

See similar equations:

| u/6=78 | | -2(5y-3)=-10y-6 | | -4(3+x)=-12 | | 17=3y-16 | | 1/2f-5=1 | | v-12=7 | | -2(3x-5)=-6x+b | | 3x-50=1000 | | 5w+11=61 | | 2/5x-1/12=3/5x-3/4 | | 7-(3x-4)=9-4x | | 3y-12=9whatisy | | 16p/4p | | -4x+6=334 | | x+0.015=8 | | (x-2)(x-1)=6+x^2 | | 3(x+4)=2x+30 | | =log(3.644) | | 13.2=2(-5.8+t) | | 3(m+2)-2(1-5m)=12(m-1)+8 | | 21+6x=69 | | g=3x+2 | | 9x+29=4x+149 | | 4(x+10)=0 | | 6(z-5)=5z | | -3(z-8)=-2z-8 | | (x-5)ln(y-4)=ln(y-4) | | x+x-5+2(x-5)=21 | | 250=n-175 | | ln(3x+4)=4.3 | | .75(68)+.25x=70 | | 43=I+19 |

Equations solver categories