24*a^2-61*a-3=0

Simple and best practice solution for 24*a^2-61*a-3=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 24*a^2-61*a-3=0 equation:


Simplifying
24a2 + -61a + -3 = 0

Reorder the terms:
-3 + -61a + 24a2 = 0

Solving
-3 + -61a + 24a2 = 0

Solving for variable 'a'.

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

Divide each side by '24'.
-0.125 + -2.541666667a + a2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -2.541666667a + 0.125 + a2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -2.541666667a + a2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -2.541666667a + a2 = 0 + 0.125
-2.541666667a + a2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-2.541666667a + a2 = 0.125

The a term is -2.541666667a.  Take half its coefficient (-1.270833334).
Square it (1.615017363) and add it to both sides.

Add '1.615017363' to each side of the equation.
-2.541666667a + 1.615017363 + a2 = 0.125 + 1.615017363

Reorder the terms:
1.615017363 + -2.541666667a + a2 = 0.125 + 1.615017363

Combine like terms: 0.125 + 1.615017363 = 1.740017363
1.615017363 + -2.541666667a + a2 = 1.740017363

Factor a perfect square on the left side:
(a + -1.270833334)(a + -1.270833334) = 1.740017363

Calculate the square root of the right side: 1.319097177

Break this problem into two subproblems by setting 
(a + -1.270833334) equal to 1.319097177 and -1.319097177.

Subproblem 1

a + -1.270833334 = 1.319097177 Simplifying a + -1.270833334 = 1.319097177 Reorder the terms: -1.270833334 + a = 1.319097177 Solving -1.270833334 + a = 1.319097177 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.270833334' to each side of the equation. -1.270833334 + 1.270833334 + a = 1.319097177 + 1.270833334 Combine like terms: -1.270833334 + 1.270833334 = 0.000000000 0.000000000 + a = 1.319097177 + 1.270833334 a = 1.319097177 + 1.270833334 Combine like terms: 1.319097177 + 1.270833334 = 2.589930511 a = 2.589930511 Simplifying a = 2.589930511

Subproblem 2

a + -1.270833334 = -1.319097177 Simplifying a + -1.270833334 = -1.319097177 Reorder the terms: -1.270833334 + a = -1.319097177 Solving -1.270833334 + a = -1.319097177 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.270833334' to each side of the equation. -1.270833334 + 1.270833334 + a = -1.319097177 + 1.270833334 Combine like terms: -1.270833334 + 1.270833334 = 0.000000000 0.000000000 + a = -1.319097177 + 1.270833334 a = -1.319097177 + 1.270833334 Combine like terms: -1.319097177 + 1.270833334 = -0.048263843 a = -0.048263843 Simplifying a = -0.048263843

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.589930511, -0.048263843}

See similar equations:

| 2b*2b= | | 3(Y-1)+4(2+b)=4b(y+1) | | 3in(2x)+2in(x)=1.5 | | 3+5(6-2)= | | 40=ln(x) | | -2x^2-19x-24=0 | | 2-(-5)+9= | | x^3+4x^2-x-2= | | 2(3x+2)=2x+4 | | 4(x-7)=-6 | | 12T^2-3+12(3-T)=T+(4T-1)(3T+1) | | y+10=-6y+3 | | -1+15-7-7= | | 9(h+3)=72 | | -5(-2y)+4(0)=20 | | y=x^3-5x^2+7x-14 | | -5x^2+30x+35=0 | | 6x^2+x+15=0 | | 4x-7=x+18 | | 5(y-10)=4y | | 21-3x=3 | | 52=10+x | | y=22x-5 | | -1.29x^2*25-140x^2-4x=0.72 | | 5(6-3y)= | | 2x*2*197=120x-85*2 | | 8(h+3)=4 | | 8(x-4)=5x-3 | | 4(h+3)=4 | | (4)(4)(4)= | | 8x+5-3x+3=36 | | 6+3x-2x=5 |

Equations solver categories