.5x(x-3)+(1.5-x)=5x

Simple and best practice solution for .5x(x-3)+(1.5-x)=5x 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-3)+(1.5-x)=5x equation:


Simplifying
0.5x(x + -3) + (1.5 + -1x) = 5x

Reorder the terms:
0.5x(-3 + x) + (1.5 + -1x) = 5x
(-3 * 0.5x + x * 0.5x) + (1.5 + -1x) = 5x
(-1.5x + 0.5x2) + (1.5 + -1x) = 5x

Remove parenthesis around (1.5 + -1x)
-1.5x + 0.5x2 + 1.5 + -1x = 5x

Reorder the terms:
1.5 + -1.5x + -1x + 0.5x2 = 5x

Combine like terms: -1.5x + -1x = -2.5x
1.5 + -2.5x + 0.5x2 = 5x

Solving
1.5 + -2.5x + 0.5x2 = 5x

Solving for variable 'x'.

Reorder the terms:
1.5 + -2.5x + -5x + 0.5x2 = 5x + -5x

Combine like terms: -2.5x + -5x = -7.5x
1.5 + -7.5x + 0.5x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
1.5 + -7.5x + 0.5x2 = 0

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

Divide each side by '0.5'.
3 + -15x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -15x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -15x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -15x + x2 = 0 + -3
-15x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-15x + x2 = -3

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -3 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -3 + 56.25

Combine like terms: -3 + 56.25 = 53.25
56.25 + -15x + x2 = 53.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 53.25

Calculate the square root of the right side: 7.29725976

Break this problem into two subproblems by setting 
(x + -7.5) equal to 7.29725976 and -7.29725976.

Subproblem 1

x + -7.5 = 7.29725976 Simplifying x + -7.5 = 7.29725976 Reorder the terms: -7.5 + x = 7.29725976 Solving -7.5 + x = 7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.29725976 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.29725976 + 7.5 x = 7.29725976 + 7.5 Combine like terms: 7.29725976 + 7.5 = 14.79725976 x = 14.79725976 Simplifying x = 14.79725976

Subproblem 2

x + -7.5 = -7.29725976 Simplifying x + -7.5 = -7.29725976 Reorder the terms: -7.5 + x = -7.29725976 Solving -7.5 + x = -7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.29725976 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.29725976 + 7.5 x = -7.29725976 + 7.5 Combine like terms: -7.29725976 + 7.5 = 0.20274024 x = 0.20274024 Simplifying x = 0.20274024

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.79725976, 0.20274024}

See similar equations:

| 4+3t=-6-2 | | -2(x+4)-5=2x+1 | | 4a+1-9a=106 | | j(0)=2x | | 10c+4=24 | | j(-4)=2x | | 1/6=-17 | | 2x-8+5x-2= | | 6x-4=-(-3x+1) | | 8y+24=7+7y | | j(0.75)=2x | | x^2-21x+9.8=0 | | 100x=(100)(7.4) | | 5x-8x= | | 2+6x=56 | | 0.03x+0.15=-0.45 | | -4x-42=-18 | | 1.3+.5x=-3.41 | | 3m-7m=16 | | 21.934=-1.1(-4.2x+1.9) | | -3(x-3)=12+x-2x | | -(y-9)= | | -33x(5+8x)=12x*2 | | 4565444+87= | | 5m-11m= | | w+30w=8800 | | -4x+1=1-1x | | 3(14)-4y=24 | | 5(4x+9x)=-3 | | 7+s=-10 | | 3(x-4)-x=4 | | 2(4+17x)=8 |

Equations solver categories