a^2-10a+13=0

Simple and best practice solution for a^2-10a+13=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 a^2-10a+13=0 equation:


Simplifying
a2 + -10a + 13 = 0

Reorder the terms:
13 + -10a + a2 = 0

Solving
13 + -10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -10a + -13 + a2 = 0 + -13

Reorder the terms:
13 + -13 + -10a + a2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -10a + a2 = 0 + -13
-10a + a2 = 0 + -13

Combine like terms: 0 + -13 = -13
-10a + a2 = -13

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = -13 + 25

Reorder the terms:
25 + -10a + a2 = -13 + 25

Combine like terms: -13 + 25 = 12
25 + -10a + a2 = 12

Factor a perfect square on the left side:
(a + -5)(a + -5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(a + -5) equal to 3.464101615 and -3.464101615.

Subproblem 1

a + -5 = 3.464101615 Simplifying a + -5 = 3.464101615 Reorder the terms: -5 + a = 3.464101615 Solving -5 + a = 3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + a = 3.464101615 + 5 a = 3.464101615 + 5 Combine like terms: 3.464101615 + 5 = 8.464101615 a = 8.464101615 Simplifying a = 8.464101615

Subproblem 2

a + -5 = -3.464101615 Simplifying a + -5 = -3.464101615 Reorder the terms: -5 + a = -3.464101615 Solving -5 + a = -3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + a = -3.464101615 + 5 a = -3.464101615 + 5 Combine like terms: -3.464101615 + 5 = 1.535898385 a = 1.535898385 Simplifying a = 1.535898385

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.464101615, 1.535898385}

See similar equations:

| 7x+6y=132 | | x(4+x)=7(x-3+7) | | -4/3x=1 | | 12y-56=6y | | 9+y=-6 | | 47=8x-7-2x-11 | | 3p-7(2p-13)=3(-2p+9) | | 47=2z | | 9/10x=1/8 | | 5+y=-6 | | 18/4 | | -12n-18=-6 | | 5+y=-12 | | 7x+71=120 | | 7x+71=120 | | -21z+12=-27 | | 4y^2-x^2=36 | | 5y-1=7y+9 | | x-8.3=-3.2 | | 2x-3(x+4)=-6 | | 2-7(3-6x)=0 | | 5+19y=9y-12 | | q^2-8q=7 | | x*x+5x=750 | | 4x^2+1120x-201600=0 | | t/-5=-8 | | 6-4-8/2 | | 12/2(6-7+4)*2=x | | 18(x+1)=2(9x-4)+26 | | 4-9(6x+5)=8 | | 18x^3+12x^2+2x=0 | | 3-5x+2x=-2-2(1-x) |

Equations solver categories