3x^2-10x-75=0

Simple and best practice solution for 3x^2-10x-75=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^2-10x-75=0 equation:


Simplifying
3x2 + -10x + -75 = 0

Reorder the terms:
-75 + -10x + 3x2 = 0

Solving
-75 + -10x + 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'.
-25 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -3.333333333x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -3.333333333x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -3.333333333x + x2 = 0 + 25
-3.333333333x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-3.333333333x + x2 = 25

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 25 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 25 + 2.777777779

Combine like terms: 25 + 2.777777779 = 27.777777779
2.777777779 + -3.333333333x + x2 = 27.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 27.777777779

Calculate the square root of the right side: 5.270462767

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 5.270462767 and -5.270462767.

Subproblem 1

x + -1.666666667 = 5.270462767 Simplifying x + -1.666666667 = 5.270462767 Reorder the terms: -1.666666667 + x = 5.270462767 Solving -1.666666667 + x = 5.270462767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 5.270462767 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 5.270462767 + 1.666666667 x = 5.270462767 + 1.666666667 Combine like terms: 5.270462767 + 1.666666667 = 6.937129434 x = 6.937129434 Simplifying x = 6.937129434

Subproblem 2

x + -1.666666667 = -5.270462767 Simplifying x + -1.666666667 = -5.270462767 Reorder the terms: -1.666666667 + x = -5.270462767 Solving -1.666666667 + x = -5.270462767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -5.270462767 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -5.270462767 + 1.666666667 x = -5.270462767 + 1.666666667 Combine like terms: -5.270462767 + 1.666666667 = -3.6037961 x = -3.6037961 Simplifying x = -3.6037961

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.937129434, -3.6037961}

See similar equations:

| (p+15)+(2p-24)+p=479 | | (4x^2)-33x+63=0 | | 0=3x^2-24x+12 | | y=3x^2-24x+12 | | 9x+15=16x^2 | | 18+3x=24+3x | | 9x+15-16x^2=0 | | 2x^2-5=-4.5 | | -16x^2-29x+4=16 | | 12t^2-22t-20=0 | | 4x^3+4x^2+x=0 | | 6x+8-2x(7-27)=2(6+1) | | 3c+2-5c=-c+3 | | (4/5)b=12 | | 9x^2-35=14 | | 107-5x^2=-18 | | 107-5x^2=18 | | -7v-1=-4(v+7) | | 4(y+7)=-7y-27 | | 3(x-7)=y | | 5x^3-2x^2-10x+4= | | 3z+2z=25-2i | | -2w+10=6(w-9) | | 10=9x-7 | | 3x^2+4y^2-6x-32y+55=0 | | 16x^3-25x=0 | | 6x-3y+18=0 | | 6-x=-10 | | 5x+16y-12z=230 | | 2y-4x-12=0 | | 10x+24y=123 | | 9x+11=7x+1 |

Equations solver categories