4a^2-6a-11=0

Simple and best practice solution for 4a^2-6a-11=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 4a^2-6a-11=0 equation:


Simplifying
4a2 + -6a + -11 = 0

Reorder the terms:
-11 + -6a + 4a2 = 0

Solving
-11 + -6a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-2.75 + -1.5a + a2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -1.5a + 2.75 + a2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -1.5a + a2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -1.5a + a2 = 0 + 2.75
-1.5a + a2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-1.5a + a2 = 2.75

The a term is -1.5a.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5a + 0.5625 + a2 = 2.75 + 0.5625

Reorder the terms:
0.5625 + -1.5a + a2 = 2.75 + 0.5625

Combine like terms: 2.75 + 0.5625 = 3.3125
0.5625 + -1.5a + a2 = 3.3125

Factor a perfect square on the left side:
(a + -0.75)(a + -0.75) = 3.3125

Calculate the square root of the right side: 1.820027472

Break this problem into two subproblems by setting 
(a + -0.75) equal to 1.820027472 and -1.820027472.

Subproblem 1

a + -0.75 = 1.820027472 Simplifying a + -0.75 = 1.820027472 Reorder the terms: -0.75 + a = 1.820027472 Solving -0.75 + a = 1.820027472 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 1.820027472 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 1.820027472 + 0.75 a = 1.820027472 + 0.75 Combine like terms: 1.820027472 + 0.75 = 2.570027472 a = 2.570027472 Simplifying a = 2.570027472

Subproblem 2

a + -0.75 = -1.820027472 Simplifying a + -0.75 = -1.820027472 Reorder the terms: -0.75 + a = -1.820027472 Solving -0.75 + a = -1.820027472 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -1.820027472 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -1.820027472 + 0.75 a = -1.820027472 + 0.75 Combine like terms: -1.820027472 + 0.75 = -1.070027472 a = -1.070027472 Simplifying a = -1.070027472

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.570027472, -1.070027472}

See similar equations:

| 1w+16=7 | | 3+x/11=7 | | 12x+15=51 | | 9(2x-4-x)+7(3-x)= | | 9-5x=64 | | 5x+4=4+3x+16 | | -98-4x=58+2x | | 1.6=tsp | | 0(2x-4-x)+7(3-x)= | | 7x-45=11x+63 | | 64x^2-36=0 | | 6x-2=20x+5 | | -178+6x=-3x+47 | | -179+6x=-3x+47 | | -3y-6=-2y-9 | | 3(x+2)+4x=6x-9 | | -12x-37=59-4x | | 3m^2-5m-12=0 | | x+26=5x+42 | | Logx=2 | | -5x-60=60+3x | | 15(10)5x+3=1200 | | 1x=16-1x | | x^2=-15x-23 | | -108-4x=6x+142 | | 10x^2+2x=-2 | | 2(1.4)x+1=926 | | 4x-51=-2x+93 | | 7x+3-2x=4+2x-7 | | 5x+5-8=3x+21 | | 5y-3=10-8y | | -17=x-7 |

Equations solver categories