4x+5x^2+12x=14x^2-10x-30

Simple and best practice solution for 4x+5x^2+12x=14x^2-10x-30 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 4x+5x^2+12x=14x^2-10x-30 equation:


Simplifying
4x + 5x2 + 12x = 14x2 + -10x + -30

Reorder the terms:
4x + 12x + 5x2 = 14x2 + -10x + -30

Combine like terms: 4x + 12x = 16x
16x + 5x2 = 14x2 + -10x + -30

Reorder the terms:
16x + 5x2 = -30 + -10x + 14x2

Solving
16x + 5x2 = -30 + -10x + 14x2

Solving for variable 'x'.

Reorder the terms:
30 + 16x + 10x + 5x2 + -14x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2

Combine like terms: 16x + 10x = 26x
30 + 26x + 5x2 + -14x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2

Combine like terms: 5x2 + -14x2 = -9x2
30 + 26x + -9x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2

Reorder the terms:
30 + 26x + -9x2 = -30 + 30 + -10x + 10x + 14x2 + -14x2

Combine like terms: -30 + 30 = 0
30 + 26x + -9x2 = 0 + -10x + 10x + 14x2 + -14x2
30 + 26x + -9x2 = -10x + 10x + 14x2 + -14x2

Combine like terms: -10x + 10x = 0
30 + 26x + -9x2 = 0 + 14x2 + -14x2
30 + 26x + -9x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
30 + 26x + -9x2 = 0

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

Divide each side by '-9'.
-3.333333333 + -2.888888889x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -2.888888889x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -2.888888889x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -2.888888889x + x2 = 0 + 3.333333333
-2.888888889x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-2.888888889x + x2 = 3.333333333

The x term is -2.888888889x.  Take half its coefficient (-1.444444445).
Square it (2.086419755) and add it to both sides.

Add '2.086419755' to each side of the equation.
-2.888888889x + 2.086419755 + x2 = 3.333333333 + 2.086419755

Reorder the terms:
2.086419755 + -2.888888889x + x2 = 3.333333333 + 2.086419755

Combine like terms: 3.333333333 + 2.086419755 = 5.419753088
2.086419755 + -2.888888889x + x2 = 5.419753088

Factor a perfect square on the left side:
(x + -1.444444445)(x + -1.444444445) = 5.419753088

Calculate the square root of the right side: 2.328036316

Break this problem into two subproblems by setting 
(x + -1.444444445) equal to 2.328036316 and -2.328036316.

Subproblem 1

x + -1.444444445 = 2.328036316 Simplifying x + -1.444444445 = 2.328036316 Reorder the terms: -1.444444445 + x = 2.328036316 Solving -1.444444445 + x = 2.328036316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = 2.328036316 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = 2.328036316 + 1.444444445 x = 2.328036316 + 1.444444445 Combine like terms: 2.328036316 + 1.444444445 = 3.772480761 x = 3.772480761 Simplifying x = 3.772480761

Subproblem 2

x + -1.444444445 = -2.328036316 Simplifying x + -1.444444445 = -2.328036316 Reorder the terms: -1.444444445 + x = -2.328036316 Solving -1.444444445 + x = -2.328036316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = -2.328036316 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = -2.328036316 + 1.444444445 x = -2.328036316 + 1.444444445 Combine like terms: -2.328036316 + 1.444444445 = -0.883591871 x = -0.883591871 Simplifying x = -0.883591871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.772480761, -0.883591871}

See similar equations:

| 3l+4l+l=13+l | | T=BD-7 | | 3=3k | | 10y-4=-16+12y | | 10=(3-2x)(5-2x) | | 12y+6y=21x+36 | | lgx+3=5 | | 26x-8x^2+30=0 | | 4(2x-4)=6 | | [2x-6]=[-8] | | (x^2)-4x-36=0 | | [2x-4]=[-12] | | -8v+7=-5v+10 | | 8-2(5v+7)= | | (-8+7i)-(8-2i)= | | 3(3x-2)=4+9 | | [2x-2]=[-16] | | 48=4(5+7n)-4(4n-7) | | 2x+2.25=5 | | x+3=-4(2x-3) | | 3x-7x=3x-12 | | 5+5x=-3 | | 2xz-5y-9z+9=6y+4z+3 | | -8(5b+8)=-344 | | H=vt-5t*5t | | 14-12= | | 9(5x-7)(1-4x)=0 | | 15x^2-25=10x | | [5+8c]-19=-9 | | 3(t-2)+t-2=-(t-10) | | (m+4)(m-10)=0 | | x+x*0.13=3928000 |

Equations solver categories