2a^2-10a=21

Simple and best practice solution for 2a^2-10a=21 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 2a^2-10a=21 equation:


Simplifying
2a2 + -10a = 21

Reorder the terms:
-10a + 2a2 = 21

Solving
-10a + 2a2 = 21

Solving for variable 'a'.

Reorder the terms:
-21 + -10a + 2a2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -10a + 2a2 = 0

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

Divide each side by '2'.
-10.5 + -5a + a2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -5a + 10.5 + a2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -5a + a2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -5a + a2 = 0 + 10.5
-5a + a2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-5a + a2 = 10.5

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = 10.5 + 6.25

Reorder the terms:
6.25 + -5a + a2 = 10.5 + 6.25

Combine like terms: 10.5 + 6.25 = 16.75
6.25 + -5a + a2 = 16.75

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 16.75

Calculate the square root of the right side: 4.092676386

Break this problem into two subproblems by setting 
(a + -2.5) equal to 4.092676386 and -4.092676386.

Subproblem 1

a + -2.5 = 4.092676386 Simplifying a + -2.5 = 4.092676386 Reorder the terms: -2.5 + a = 4.092676386 Solving -2.5 + a = 4.092676386 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 4.092676386 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 4.092676386 + 2.5 a = 4.092676386 + 2.5 Combine like terms: 4.092676386 + 2.5 = 6.592676386 a = 6.592676386 Simplifying a = 6.592676386

Subproblem 2

a + -2.5 = -4.092676386 Simplifying a + -2.5 = -4.092676386 Reorder the terms: -2.5 + a = -4.092676386 Solving -2.5 + a = -4.092676386 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -4.092676386 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -4.092676386 + 2.5 a = -4.092676386 + 2.5 Combine like terms: -4.092676386 + 2.5 = -1.592676386 a = -1.592676386 Simplifying a = -1.592676386

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.592676386, -1.592676386}

See similar equations:

| -9x+x^2=14 | | 4+x-3(X-1)=13 | | 4(y+8)-3(y+5)=(3y+1) | | 14m-1=2m-8 | | 4y+-2y=10 | | 2n(3n+6)= | | 147=21 | | 5x+3x-4x=32 | | y/3=45 | | 5x+37=2x+10 | | 3*12+x=82 | | 25=3(x+4) | | Log(x+1)=log(x-1)+3 | | x-2=3x+16 | | 2u+1=17 | | w+2x=2w+3y+x+3z | | 21-6x=7(3-2x)-8x | | Y=57-3*6000 | | 5x+57=x+21 | | 133+16m=405 | | 33n-190=437 | | 4x+36=x+12 | | Y=50-2*7000 | | -3x+39=x+3 | | Y=54-2*7000 | | -x/3=13/2 | | 19.3=m/96.5 | | 19.3=m/96.3 | | Y=51-2*5000 | | 0.06(x+8)=0.03(2x+8)+024 | | 9w+5=8w | | -25x^2+9y^2+225=0 |

Equations solver categories