4x^2-27x-162=0

Simple and best practice solution for 4x^2-27x-162=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 4x^2-27x-162=0 equation:


Simplifying
4x2 + -27x + -162 = 0

Reorder the terms:
-162 + -27x + 4x2 = 0

Solving
-162 + -27x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-40.5 + -6.75x + x2 = 0

Move the constant term to the right:

Add '40.5' to each side of the equation.
-40.5 + -6.75x + 40.5 + x2 = 0 + 40.5

Reorder the terms:
-40.5 + 40.5 + -6.75x + x2 = 0 + 40.5

Combine like terms: -40.5 + 40.5 = 0.0
0.0 + -6.75x + x2 = 0 + 40.5
-6.75x + x2 = 0 + 40.5

Combine like terms: 0 + 40.5 = 40.5
-6.75x + x2 = 40.5

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = 40.5 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = 40.5 + 11.390625

Combine like terms: 40.5 + 11.390625 = 51.890625
11.390625 + -6.75x + x2 = 51.890625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 51.890625

Calculate the square root of the right side: 7.203514767

Break this problem into two subproblems by setting 
(x + -3.375) equal to 7.203514767 and -7.203514767.

Subproblem 1

x + -3.375 = 7.203514767 Simplifying x + -3.375 = 7.203514767 Reorder the terms: -3.375 + x = 7.203514767 Solving -3.375 + x = 7.203514767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 7.203514767 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 7.203514767 + 3.375 x = 7.203514767 + 3.375 Combine like terms: 7.203514767 + 3.375 = 10.578514767 x = 10.578514767 Simplifying x = 10.578514767

Subproblem 2

x + -3.375 = -7.203514767 Simplifying x + -3.375 = -7.203514767 Reorder the terms: -3.375 + x = -7.203514767 Solving -3.375 + x = -7.203514767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -7.203514767 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -7.203514767 + 3.375 x = -7.203514767 + 3.375 Combine like terms: -7.203514767 + 3.375 = -3.828514767 x = -3.828514767 Simplifying x = -3.828514767

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.578514767, -3.828514767}

See similar equations:

| cx+dX=f | | 29-4x=25 | | 7y-22=80y-44 | | 1.2n=0.8 | | -1=5(1/2)+b | | 12n=4.8 | | 24-y=8y-11 | | 2x+4+2x+8=36 | | ln(x/6)=-9.45 | | 5n^2-26n+24=0 | | 44(2+4)=222-16 | | ln(x/6)=9.45 | | 13r=34 | | 3x^2+7x-12=o | | 4x=2x/3+2 | | 2y-14=2-16y-4 | | y^2-4y+4=2y^2-6y+1 | | n^2+2n+29=4 | | (5m-2)(4m+7)= | | 4/(2+3i) | | 240=(x+2)x | | 1000(1+6%/4)20= | | 5x+5/x-3=120/x^2-9+5x-5/x+3 | | -1--1= | | 24=(-x-3) | | b^3+4b^2+3=0 | | 10*5/12 | | x/7+x-7+13x/x^2-49 | | -20-[-5-3(-2+1)]= | | 16+5*3-1+100/2-40+50/5 | | 9x-5=8(x-4)+6 | | 11x+6=10(x+5)-10 |

Equations solver categories