9x^2-30x+23=0

Simple and best practice solution for 9x^2-30x+23=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 9x^2-30x+23=0 equation:


Simplifying
9x2 + -30x + 23 = 0

Reorder the terms:
23 + -30x + 9x2 = 0

Solving
23 + -30x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
2.555555556 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.555555556' to each side of the equation.
2.555555556 + -3.333333333x + -2.555555556 + x2 = 0 + -2.555555556

Reorder the terms:
2.555555556 + -2.555555556 + -3.333333333x + x2 = 0 + -2.555555556

Combine like terms: 2.555555556 + -2.555555556 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + -2.555555556
-3.333333333x + x2 = 0 + -2.555555556

Combine like terms: 0 + -2.555555556 = -2.555555556
-3.333333333x + x2 = -2.555555556

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 = -2.555555556 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -2.555555556 + 2.777777779

Combine like terms: -2.555555556 + 2.777777779 = 0.222222223
2.777777779 + -3.333333333x + x2 = 0.222222223

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 0.222222223

Calculate the square root of the right side: 0.471404522

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 0.471404522 and -0.471404522.

Subproblem 1

x + -1.666666667 = 0.471404522 Simplifying x + -1.666666667 = 0.471404522 Reorder the terms: -1.666666667 + x = 0.471404522 Solving -1.666666667 + x = 0.471404522 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 = 0.471404522 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 0.471404522 + 1.666666667 x = 0.471404522 + 1.666666667 Combine like terms: 0.471404522 + 1.666666667 = 2.138071189 x = 2.138071189 Simplifying x = 2.138071189

Subproblem 2

x + -1.666666667 = -0.471404522 Simplifying x + -1.666666667 = -0.471404522 Reorder the terms: -1.666666667 + x = -0.471404522 Solving -1.666666667 + x = -0.471404522 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 = -0.471404522 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -0.471404522 + 1.666666667 x = -0.471404522 + 1.666666667 Combine like terms: -0.471404522 + 1.666666667 = 1.195262145 x = 1.195262145 Simplifying x = 1.195262145

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.138071189, 1.195262145}

See similar equations:

| 8(2m+1)= | | -9-8=10x+10-9x | | x+0.25=-1.25 | | 3(-2.5y+7)=-36 | | -2(4-x)-7=15 | | 12(p+5)=13p+2 | | 44=5x-3x | | 3(y-5)=-3y | | 8x-5-2x+5=x-18+8x | | 2x+15=95 | | 22+3x=-4(5-6x) | | 32=4 | | 10p-45=3(p-15) | | -3(a+5)+9=15 | | 1-6n+n=9 | | 45+-.5y+3(45-.5Y)+2Y=180 | | 5x+28=20x | | 293.92=17.6h | | 25=5 | | x^2+y^2+4y-12=0 | | s=56s=t÷6 | | 14d-21=6d+3 | | 4(h-5g)= | | 5m+3n=14 | | 6v^2-7v+2=0 | | 2-18y^2=0 | | 3x-2y=-36 | | 2x-3x=-3-8 | | ab-6c=5 | | 5+3(q-4)=2(q-4) | | 2(5a-13)=47 | | x-16=21 |

Equations solver categories