1a^2-2a-7=0

Simple and best practice solution for 1a^2-2a-7=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 1a^2-2a-7=0 equation:


Simplifying
1a2 + -2a + -7 = 0

Reorder the terms:
-7 + -2a + 1a2 = 0

Solving
-7 + -2a + 1a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2a + 7 + a2 = 0 + 7

Reorder the terms:
-7 + 7 + -2a + a2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2a + a2 = 0 + 7
-2a + a2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2a + a2 = 7

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 7 + 1

Reorder the terms:
1 + -2a + a2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + -2a + a2 = 8

Factor a perfect square on the left side:
(a + -1)(a + -1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(a + -1) equal to 2.828427125 and -2.828427125.

Subproblem 1

a + -1 = 2.828427125 Simplifying a + -1 = 2.828427125 Reorder the terms: -1 + a = 2.828427125 Solving -1 + a = 2.828427125 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.828427125 + 1 a = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 a = 3.828427125 Simplifying a = 3.828427125

Subproblem 2

a + -1 = -2.828427125 Simplifying a + -1 = -2.828427125 Reorder the terms: -1 + a = -2.828427125 Solving -1 + a = -2.828427125 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.828427125 + 1 a = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 a = -1.828427125 Simplifying a = -1.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.828427125, -1.828427125}

See similar equations:

| 9x+-34=-88 | | 7x+28-4x-4=5 | | x=2mx-8b | | -5(5x-3)-27=-3(3x-2) | | 7b-4(3b+7)=7-(8+8b) | | -9x-16=-1 | | 5(x-3)=3x+4+2(5-x) | | .4t+1.7=1.3 | | 8y^2+105y+13= | | -27-3x^2=0 | | 6+r=4 | | 5m-7=1+7m | | 5(4x-3)=-25 | | 4(x-2)=2(x+10) | | 152+2h=972 | | y-9+2=6 | | 21+5x=-34 | | 9+3.5g=11-.5g | | 9x+37=91 | | 7x-2(5x+9)=7-(11-11x) | | 69r+69= | | n-3(3)=14-4(3) | | 22(6-v)+6v=148 | | (x-2)*2=49 | | n-3(2)=14-4(2) | | 3v+6=7 | | 41c-41d= | | (a+1)*2=25 | | 7r-4r+5=9r+5-r | | 3x^2+18x+7=0 | | 0=(6-7x)10 | | (x-2)(y+3)=35 |

Equations solver categories