2x^2-45x+180=0

Simple and best practice solution for 2x^2-45x+180=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 2x^2-45x+180=0 equation:


Simplifying
2x2 + -45x + 180 = 0

Reorder the terms:
180 + -45x + 2x2 = 0

Solving
180 + -45x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
90 + -22.5x + x2 = 0

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + -22.5x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + -22.5x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -22.5x + x2 = 0 + -90
-22.5x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
-22.5x + x2 = -90

The x term is -22.5x.  Take half its coefficient (-11.25).
Square it (126.5625) and add it to both sides.

Add '126.5625' to each side of the equation.
-22.5x + 126.5625 + x2 = -90 + 126.5625

Reorder the terms:
126.5625 + -22.5x + x2 = -90 + 126.5625

Combine like terms: -90 + 126.5625 = 36.5625
126.5625 + -22.5x + x2 = 36.5625

Factor a perfect square on the left side:
(x + -11.25)(x + -11.25) = 36.5625

Calculate the square root of the right side: 6.046693311

Break this problem into two subproblems by setting 
(x + -11.25) equal to 6.046693311 and -6.046693311.

Subproblem 1

x + -11.25 = 6.046693311 Simplifying x + -11.25 = 6.046693311 Reorder the terms: -11.25 + x = 6.046693311 Solving -11.25 + x = 6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 6.046693311 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 6.046693311 + 11.25 x = 6.046693311 + 11.25 Combine like terms: 6.046693311 + 11.25 = 17.296693311 x = 17.296693311 Simplifying x = 17.296693311

Subproblem 2

x + -11.25 = -6.046693311 Simplifying x + -11.25 = -6.046693311 Reorder the terms: -11.25 + x = -6.046693311 Solving -11.25 + x = -6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -6.046693311 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -6.046693311 + 11.25 x = -6.046693311 + 11.25 Combine like terms: -6.046693311 + 11.25 = 5.203306689 x = 5.203306689 Simplifying x = 5.203306689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.296693311, 5.203306689}

See similar equations:

| -102=51x | | 2n+7=9 | | 3(11x+2)=33x-10 | | 3v-2=22 | | 40.32=.768n | | 40+6x-10=180 | | -3v+3=-21 | | j-80/4=3 | | 5x-y=31 | | 22=4/3x-6 | | T+10+T=T+20 | | 5p+5=-40 | | 21n=88.83 | | 4x-5=-14 | | 2+73=n | | 2+685=85n | | 4/25=x/1250 | | (-5x-3)(6-9)=2x+4 | | (5x-3)(6-9)=2x+6 | | 16+7.3x-9x=2x-9.5+7 | | 5v-4=-24 | | -5609.00+200.00x=-2800 | | 3[x+7]=21-12x | | (1/2)^3x-8^2 | | 4x+19+7x-15=180 | | x-4=5[x+2] | | 8x+12-0.5x=4 | | (2x-7)+(4x-9)= | | 4x+3y=9x-8 | | -2y+45=7y | | 5x-6=11x-42 | | 5x-6=11-42 |

Equations solver categories