3x^2-7x-60=0

Simple and best practice solution for 3x^2-7x-60=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-60=0 equation: 


Simplifying
3x2 + -7x + -60 = 0

Reorder the terms:
-60 + -7x + 3x2 = 0

Solving
-60 + -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'.
-20 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2.333333333x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -2.333333333x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2.333333333x + x2 = 0 + 20
-2.333333333x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2.333333333x + x2 = 20

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 = 20 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 20 + 1.361111112

Combine like terms: 20 + 1.361111112 = 21.361111112
1.361111112 + -2.333333333x + x2 = 21.361111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 21.361111112

Calculate the square root of the right side: 4.621808208

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 4.621808208 and -4.621808208.


Subproblem 1
x + -1.166666667 = 4.621808208

Simplifying
x + -1.166666667 = 4.621808208

Reorder the terms:
-1.166666667 + x = 4.621808208

Solving
-1.166666667 + x = 4.621808208

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 = 4.621808208 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 4.621808208 + 1.166666667
x = 4.621808208 + 1.166666667

Combine like terms: 4.621808208 + 1.166666667 = 5.788474875
x = 5.788474875

Simplifying
x = 5.788474875


Subproblem 2
x + -1.166666667 = -4.621808208

Simplifying
x + -1.166666667 = -4.621808208

Reorder the terms:
-1.166666667 + x = -4.621808208

Solving
-1.166666667 + x = -4.621808208

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 = -4.621808208 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -4.621808208 + 1.166666667
x = -4.621808208 + 1.166666667

Combine like terms: -4.621808208 + 1.166666667 = -3.455141541
x = -3.455141541

Simplifying
x = -3.455141541


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.788474875, -3.455141541}

See similar equations:

| (6-2x)(13-2x)(x)=0 | | 51/3-35/12= | | 0.7-0.02x=0.1 | | -5v+45=5(v-7) | | 9(u+9)=-3u+33 | | -7x-5/3=4-36/7x | | 9k-3k=27 | | 4x=-6y+12 | | v=4/3*3.14*(3)3 | | 9(u+9)=-3+33 | | -3y-5=-7 | | -101=-5x-6x+9 | | 152=x | | 3w+22=5(w+4) | | 12=-18+-3x | | 9=18y | | 21-6(-16)=117 | | 6(v+8)=9v+39 | | v=4/3*3.14*(4)3 | | -7x-(5/3)=4-(36/7)x | | 30=21m | | 3x=3y+6 | | 4(9x-4)-[2(5x-3)+1]= | | a^2+ab-72b^2= | | 6(x-7)=7x-9 | | 9xy-1= | | 129=.006A^2-.02A+120 | | 21-6(n)=117 | | 6v+45=9(v+2) | | -100x^2+50x+100=0 | | 3/2x=-15 | | x^2-0.9x+0.2=3 |

Equations solver categories