(3x-5)(x+5)=5

Simple and best practice solution for (3x-5)(x+5)=5 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-5)(x+5)=5 equation:


Simplifying
(3x + -5)(x + 5) = 5

Reorder the terms:
(-5 + 3x)(x + 5) = 5

Reorder the terms:
(-5 + 3x)(5 + x) = 5

Multiply (-5 + 3x) * (5 + x)
(-5(5 + x) + 3x * (5 + x)) = 5
((5 * -5 + x * -5) + 3x * (5 + x)) = 5
((-25 + -5x) + 3x * (5 + x)) = 5
(-25 + -5x + (5 * 3x + x * 3x)) = 5
(-25 + -5x + (15x + 3x2)) = 5

Combine like terms: -5x + 15x = 10x
(-25 + 10x + 3x2) = 5

Solving
-25 + 10x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
-25 + -5 + 10x + 3x2 = 5 + -5

Combine like terms: -25 + -5 = -30
-30 + 10x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-30 + 10x + 3x2 = 0

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

Divide each side by '3'.
-10 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 3.333333333x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 3.333333333x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3.333333333x + x2 = 0 + 10
3.333333333x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
3.333333333x + x2 = 10

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 = 10 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 10 + 2.777777779

Combine like terms: 10 + 2.777777779 = 12.777777779
2.777777779 + 3.333333333x + x2 = 12.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 12.777777779

Calculate the square root of the right side: 3.574601765

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 3.574601765 and -3.574601765.

Subproblem 1

x + 1.666666667 = 3.574601765 Simplifying x + 1.666666667 = 3.574601765 Reorder the terms: 1.666666667 + x = 3.574601765 Solving 1.666666667 + x = 3.574601765 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 = 3.574601765 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 3.574601765 + -1.666666667 x = 3.574601765 + -1.666666667 Combine like terms: 3.574601765 + -1.666666667 = 1.907935098 x = 1.907935098 Simplifying x = 1.907935098

Subproblem 2

x + 1.666666667 = -3.574601765 Simplifying x + 1.666666667 = -3.574601765 Reorder the terms: 1.666666667 + x = -3.574601765 Solving 1.666666667 + x = -3.574601765 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 = -3.574601765 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -3.574601765 + -1.666666667 x = -3.574601765 + -1.666666667 Combine like terms: -3.574601765 + -1.666666667 = -5.241268432 x = -5.241268432 Simplifying x = -5.241268432

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.907935098, -5.241268432}

See similar equations:

| 5x(2+3)=45 | | 4x-7=5x-15 | | 14-3x=8x+6 | | (10)/(2)y-13=-3 | | .06h=45.84 | | 5q+4(-5+3q)=1-q | | 6j-10=4j-4 | | 3(4y-1)=2(5y-7) | | 4s=168 | | 100+12x=23x | | 22-8x=10+4x | | 3(x+1)=2x-4 | | -2(2m+6)=-9m+28 | | -11+10(x+10)=4-5(2p+11) | | 7[5]-2[-4]= | | 2r+200=200 | | 9x+x=9x+4 | | 4.4m=198 | | y=82x+150 | | (8+3y)=38-7y | | 6-8x=5x-8x-29 | | 4(2+2a)=5a-1 | | 6x^5-2x^4+x^2+3= | | 0.42k=4.2 | | -2x+3=16 | | 1.4(2x-1)+1.4=0.7(4x-10) | | 3(x-1)=x+1 | | 14-(4q+5)=-2q+9 | | 6p=-24 | | -4(2b+8)=16-6b | | (x)/(3)-3=-6 | | 4-2m+8m=20 |

Equations solver categories