3x^2-7x-27=0

Simple and best practice solution for 3x^2-7x-27=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 3x^2-7x-27=0 equation:


Simplifying
3x2 + -7x + -27 = 0

Reorder the terms:
-27 + -7x + 3x2 = 0

Solving
-27 + -7x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-9 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2.333333333x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -2.333333333x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2.333333333x + x2 = 0 + 9
-2.333333333x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2.333333333x + x2 = 9

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 9 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 9 + 1.361111112

Combine like terms: 9 + 1.361111112 = 10.361111112
1.361111112 + -2.333333333x + x2 = 10.361111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 10.361111112

Calculate the square root of the right side: 3.218867986

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 3.218867986 and -3.218867986.

Subproblem 1

x + -1.166666667 = 3.218867986 Simplifying x + -1.166666667 = 3.218867986 Reorder the terms: -1.166666667 + x = 3.218867986 Solving -1.166666667 + x = 3.218867986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 3.218867986 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 3.218867986 + 1.166666667 x = 3.218867986 + 1.166666667 Combine like terms: 3.218867986 + 1.166666667 = 4.385534653 x = 4.385534653 Simplifying x = 4.385534653

Subproblem 2

x + -1.166666667 = -3.218867986 Simplifying x + -1.166666667 = -3.218867986 Reorder the terms: -1.166666667 + x = -3.218867986 Solving -1.166666667 + x = -3.218867986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -3.218867986 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -3.218867986 + 1.166666667 x = -3.218867986 + 1.166666667 Combine like terms: -3.218867986 + 1.166666667 = -2.052201319 x = -2.052201319 Simplifying x = -2.052201319

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.385534653, -2.052201319}

See similar equations:

| 1/2x2/5x81/2= | | -28-7k=-2(7k-7) | | -4a+8d=d-17 | | 11x-2+130x= | | 7a-6a+a-2=16 | | 5-3a=5(7a+s)-5 | | 3(x)=2.40(x-3) | | 2d+d-d=14 | | 5x+9.65=4x | | A=6x-48+4x+38 | | 26+10x=-64 | | -8(1+4n)=-34-6n | | =X^2+12x-45 | | 7(m+2)=35m | | 11x+5=7x-9 | | V=e/it | | 10m-7m-2m=8 | | 4x-2x-5=1 | | -14=-0.7m | | -5(2a+7)=-39-8a | | 35x/-7 | | -15p+-2p+10p+-2p+5p=16 | | -5x-34=36 | | (-3x+7)= | | 14=u/-4 | | -16*(2/5) | | -9p+20p+15p+-10p=-16 | | -8(-4n+3)=7n+26 | | 14=4/-4 | | A=-48+6x | | 150/140 | | -38/4 |

Equations solver categories