5x(x-5)=x(4x+6)-52

Simple and best practice solution for 5x(x-5)=x(4x+6)-52 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 5x(x-5)=x(4x+6)-52 equation:


Simplifying
5x(x + -5) = x(4x + 6) + -52

Reorder the terms:
5x(-5 + x) = x(4x + 6) + -52
(-5 * 5x + x * 5x) = x(4x + 6) + -52
(-25x + 5x2) = x(4x + 6) + -52

Reorder the terms:
-25x + 5x2 = x(6 + 4x) + -52
-25x + 5x2 = (6 * x + 4x * x) + -52
-25x + 5x2 = (6x + 4x2) + -52

Reorder the terms:
-25x + 5x2 = -52 + 6x + 4x2

Solving
-25x + 5x2 = -52 + 6x + 4x2

Solving for variable 'x'.

Reorder the terms:
52 + -25x + -6x + 5x2 + -4x2 = -52 + 6x + 4x2 + 52 + -6x + -4x2

Combine like terms: -25x + -6x = -31x
52 + -31x + 5x2 + -4x2 = -52 + 6x + 4x2 + 52 + -6x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
52 + -31x + 1x2 = -52 + 6x + 4x2 + 52 + -6x + -4x2

Reorder the terms:
52 + -31x + 1x2 = -52 + 52 + 6x + -6x + 4x2 + -4x2

Combine like terms: -52 + 52 = 0
52 + -31x + 1x2 = 0 + 6x + -6x + 4x2 + -4x2
52 + -31x + 1x2 = 6x + -6x + 4x2 + -4x2

Combine like terms: 6x + -6x = 0
52 + -31x + 1x2 = 0 + 4x2 + -4x2
52 + -31x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
52 + -31x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + -31x + -52 + x2 = 0 + -52

Reorder the terms:
52 + -52 + -31x + x2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -31x + x2 = 0 + -52
-31x + x2 = 0 + -52

Combine like terms: 0 + -52 = -52
-31x + x2 = -52

The x term is -31x.  Take half its coefficient (-15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
-31x + 240.25 + x2 = -52 + 240.25

Reorder the terms:
240.25 + -31x + x2 = -52 + 240.25

Combine like terms: -52 + 240.25 = 188.25
240.25 + -31x + x2 = 188.25

Factor a perfect square on the left side:
(x + -15.5)(x + -15.5) = 188.25

Calculate the square root of the right side: 13.720422734

Break this problem into two subproblems by setting 
(x + -15.5) equal to 13.720422734 and -13.720422734.

Subproblem 1

x + -15.5 = 13.720422734 Simplifying x + -15.5 = 13.720422734 Reorder the terms: -15.5 + x = 13.720422734 Solving -15.5 + x = 13.720422734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 13.720422734 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 13.720422734 + 15.5 x = 13.720422734 + 15.5 Combine like terms: 13.720422734 + 15.5 = 29.220422734 x = 29.220422734 Simplifying x = 29.220422734

Subproblem 2

x + -15.5 = -13.720422734 Simplifying x + -15.5 = -13.720422734 Reorder the terms: -15.5 + x = -13.720422734 Solving -15.5 + x = -13.720422734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -13.720422734 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -13.720422734 + 15.5 x = -13.720422734 + 15.5 Combine like terms: -13.720422734 + 15.5 = 1.779577266 x = 1.779577266 Simplifying x = 1.779577266

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.220422734, 1.779577266}

See similar equations:

| (x+4)(x-4)(2x-1)=0 | | -6a^2+7a-20=0 | | 4x^2-44x-24=0 | | 25x^3-4x=0 | | x+3=47 | | 12a=96 | | 12x^2+2x+2=0 | | a+b-2ab= | | x^3+2x^2-x=0 | | 8y-3=189 | | 9x-84=116-11x | | 5x(8-3)*(4-3)=10 | | 44-4(3+7)= | | x^3+9x^2-2x-4=0 | | p^2-7p+k= | | -4(x-6)=-4(x+6) | | x^2=x^3 | | 8x+3=c | | x^3-2x^2-3x+6=0 | | 4x-7=8-(5x-3) | | 2x^2-20x+56=0 | | 5-2(6x+1)=(4x-5)(2)-7 | | 5x+17-3x+17=6 | | [18-m]+4=21 | | a^6+17a^3+60= | | 4x^2-4x+1-14(2X-1)+40= | | 4x-12=x-3x+9 | | 11x-7=7x+13 | | 5b^8+3b^4-14= | | v^2+6v+9+8(v+3)+15= | | 3x-14=x+12 | | 3(x-5)-15=48 |

Equations solver categories