x(5x+4)=2x^2-3x+2

Simple and best practice solution for x(5x+4)=2x^2-3x+2 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 x(5x+4)=2x^2-3x+2 equation: 


Simplifying
x(5x + 4) = 2x2 + -3x + 2

Reorder the terms:
x(4 + 5x) = 2x2 + -3x + 2
(4 * x + 5x * x) = 2x2 + -3x + 2
(4x + 5x2) = 2x2 + -3x + 2

Reorder the terms:
4x + 5x2 = 2 + -3x + 2x2

Solving
4x + 5x2 = 2 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 4x + 3x + 5x2 + -2x2 = 2 + -3x + 2x2 + -2 + 3x + -2x2

Combine like terms: 4x + 3x = 7x
-2 + 7x + 5x2 + -2x2 = 2 + -3x + 2x2 + -2 + 3x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-2 + 7x + 3x2 = 2 + -3x + 2x2 + -2 + 3x + -2x2

Reorder the terms:
-2 + 7x + 3x2 = 2 + -2 + -3x + 3x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
-2 + 7x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2
-2 + 7x + 3x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-2 + 7x + 3x2 = 0 + 2x2 + -2x2
-2 + 7x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2 + 7x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 2.333333333x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 2.333333333x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 2.333333333x + x2 = 0 + 0.6666666667
2.333333333x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
2.333333333x + x2 = 0.6666666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 0.6666666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 0.6666666667 + 1.361111112

Combine like terms: 0.6666666667 + 1.361111112 = 2.0277777787
1.361111112 + 2.333333333x + x2 = 2.0277777787

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 2.0277777787

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.424000625 and -1.424000625.


Subproblem 1
x + 1.166666667 = 1.424000625

Simplifying
x + 1.166666667 = 1.424000625

Reorder the terms:
1.166666667 + x = 1.424000625

Solving
1.166666667 + x = 1.424000625

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.424000625 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.424000625 + -1.166666667
x = 1.424000625 + -1.166666667

Combine like terms: 1.424000625 + -1.166666667 = 0.257333958
x = 0.257333958

Simplifying
x = 0.257333958


Subproblem 2
x + 1.166666667 = -1.424000625

Simplifying
x + 1.166666667 = -1.424000625

Reorder the terms:
1.166666667 + x = -1.424000625

Solving
1.166666667 + x = -1.424000625

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.424000625 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.424000625 + -1.166666667
x = -1.424000625 + -1.166666667

Combine like terms: -1.424000625 + -1.166666667 = -2.590667292
x = -2.590667292

Simplifying
x = -2.590667292


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.257333958, -2.590667292}

See similar equations:

| 2(x+3)/5=4x-5 | | 0*3.2+15.75=m | | (k+4)/(8)/(3k-2)/(4k) | | (2x^2-9x+1)+(-4x^2+6x-3)= | | 2x-3=7x | | 180-x=x^2 | | 20*3.2+15.75=m | | 11x/3+11x=23 | | 3.2*2.5-10=p | | -u+2=-13 | | -u/7+2=13 | | 306/(8-0.1x) | | -3*3-4=y | | 3x^2-2x+k=0 | | 4*3-4=y | | (a^2-3a+5)(a^2+7a-2)= | | (x-1)(x^2-x-12)=0 | | 7(x-3)=6y | | 4/21-2/9 | | 1/2*95*120 | | e^9x=6 | | b=8/2-2 | | 3/4+1/12 | | p=-(0)+6 | | p=-(-1)+6 | | 43/4+21/12 | | 3x=x+5/2 | | 3(x+4)+5x-7=6+2x-2(x-4) | | p=-(-3)+6 | | -(8y+1)-(-7y-6)=3 | | x(10x-2)=9 | | 12xy-10xy^2=g |

Equations solver categories