9a^2-24a=-13

Simple and best practice solution for 9a^2-24a=-13 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 9a^2-24a=-13 equation:


Simplifying
9a2 + -24a = -13

Reorder the terms:
-24a + 9a2 = -13

Solving
-24a + 9a2 = -13

Solving for variable 'a'.

Reorder the terms:
13 + -24a + 9a2 = -13 + 13

Combine like terms: -13 + 13 = 0
13 + -24a + 9a2 = 0

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

Divide each side by '9'.
1.444444444 + -2.666666667a + a2 = 0

Move the constant term to the right:

Add '-1.444444444' to each side of the equation.
1.444444444 + -2.666666667a + -1.444444444 + a2 = 0 + -1.444444444

Reorder the terms:
1.444444444 + -1.444444444 + -2.666666667a + a2 = 0 + -1.444444444

Combine like terms: 1.444444444 + -1.444444444 = 0.000000000
0.000000000 + -2.666666667a + a2 = 0 + -1.444444444
-2.666666667a + a2 = 0 + -1.444444444

Combine like terms: 0 + -1.444444444 = -1.444444444
-2.666666667a + a2 = -1.444444444

The a term is -2.666666667a.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667a + 1.777777780 + a2 = -1.444444444 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667a + a2 = -1.444444444 + 1.777777780

Combine like terms: -1.444444444 + 1.777777780 = 0.333333336
1.777777780 + -2.666666667a + a2 = 0.333333336

Factor a perfect square on the left side:
(a + -1.333333334)(a + -1.333333334) = 0.333333336

Calculate the square root of the right side: 0.577350271

Break this problem into two subproblems by setting 
(a + -1.333333334) equal to 0.577350271 and -0.577350271.

Subproblem 1

a + -1.333333334 = 0.577350271 Simplifying a + -1.333333334 = 0.577350271 Reorder the terms: -1.333333334 + a = 0.577350271 Solving -1.333333334 + a = 0.577350271 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + a = 0.577350271 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + a = 0.577350271 + 1.333333334 a = 0.577350271 + 1.333333334 Combine like terms: 0.577350271 + 1.333333334 = 1.910683605 a = 1.910683605 Simplifying a = 1.910683605

Subproblem 2

a + -1.333333334 = -0.577350271 Simplifying a + -1.333333334 = -0.577350271 Reorder the terms: -1.333333334 + a = -0.577350271 Solving -1.333333334 + a = -0.577350271 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + a = -0.577350271 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + a = -0.577350271 + 1.333333334 a = -0.577350271 + 1.333333334 Combine like terms: -0.577350271 + 1.333333334 = 0.755983063 a = 0.755983063 Simplifying a = 0.755983063

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.910683605, 0.755983063}

See similar equations:

| 9t-5t=-24 | | 3x+23=12x-85 | | 25-3c=10 | | 5x-2x-1=15 | | -34-3x=11-8x | | 9x-39x+42=0 | | x-15x+56=0 | | 2p+5q=58 | | x+8x+7=0 | | 6x^2-10x-9=0 | | x+x-12=0 | | 5x^3+20x^2+20x=0 | | 3x+1=-7+5x | | -7(-2x+2)=-126 | | 3(2a+3)=5(2a+1) | | 2x+5=69-6x | | 11x-7y=0 | | 6(1x-9)=0 | | 6+11x=96+x | | -3(2h+2)=(h+5) | | X^2-4X-21= | | 9+6x=-x+37 | | a^2-17a+30=0 | | 19b*2c*(-a)=z | | -26-10t= | | 2X^2-75X+532=0 | | 5(2+6x)=-50 | | x^2+4-12=0 | | 3(c-5)=2(c-3) | | -7x-2=-4x+22 | | 6x(9-4)+11= | | 7.023x=31.6035 |

Equations solver categories