1.5x+5=2x^2+12x+13

Simple and best practice solution for 1.5x+5=2x^2+12x+13 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 1.5x+5=2x^2+12x+13 equation:


Simplifying
1.5x + 5 = 2x2 + 12x + 13

Reorder the terms:
5 + 1.5x = 2x2 + 12x + 13

Reorder the terms:
5 + 1.5x = 13 + 12x + 2x2

Solving
5 + 1.5x = 13 + 12x + 2x2

Solving for variable 'x'.

Reorder the terms:
5 + -13 + 1.5x + -12x + -2x2 = 13 + 12x + 2x2 + -13 + -12x + -2x2

Combine like terms: 5 + -13 = -8
-8 + 1.5x + -12x + -2x2 = 13 + 12x + 2x2 + -13 + -12x + -2x2

Combine like terms: 1.5x + -12x = -10.5x
-8 + -10.5x + -2x2 = 13 + 12x + 2x2 + -13 + -12x + -2x2

Reorder the terms:
-8 + -10.5x + -2x2 = 13 + -13 + 12x + -12x + 2x2 + -2x2

Combine like terms: 13 + -13 = 0
-8 + -10.5x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2
-8 + -10.5x + -2x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-8 + -10.5x + -2x2 = 0 + 2x2 + -2x2
-8 + -10.5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + -10.5x + -2x2 = 0

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

Divide each side by '-2'.
4 + 5.25x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 5.25x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 5.25x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5.25x + x2 = 0 + -4
5.25x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
5.25x + x2 = -4

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = -4 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = -4 + 6.890625

Combine like terms: -4 + 6.890625 = 2.890625
6.890625 + 5.25x + x2 = 2.890625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(x + 2.625) equal to 1.700183814 and -1.700183814.

Subproblem 1

x + 2.625 = 1.700183814 Simplifying x + 2.625 = 1.700183814 Reorder the terms: 2.625 + x = 1.700183814 Solving 2.625 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 1.700183814 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 1.700183814 + -2.625 x = 1.700183814 + -2.625 Combine like terms: 1.700183814 + -2.625 = -0.924816186 x = -0.924816186 Simplifying x = -0.924816186

Subproblem 2

x + 2.625 = -1.700183814 Simplifying x + 2.625 = -1.700183814 Reorder the terms: 2.625 + x = -1.700183814 Solving 2.625 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -1.700183814 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -1.700183814 + -2.625 x = -1.700183814 + -2.625 Combine like terms: -1.700183814 + -2.625 = -4.325183814 x = -4.325183814 Simplifying x = -4.325183814

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.924816186, -4.325183814}

See similar equations:

| (4/9)-(n/9)=4/9 | | 6+j/2=4 | | 4/9-n/9=4/9 | | 6t-1=9t-36 | | 8/3x3/8=40(3/8) | | 7385-97x=6250 | | 10d-2t=-40 | | -2x+7=2x^2+3x-5 | | -5+/3=0 | | 156+38=x | | 3x+2x+10+9=2x+8 | | 4(8x-14)=9 | | 1996-43x=3200 | | 78/2 | | -5(-6+5v)=130 | | 4+2x=-5x+25 | | 1/2=9+y1/4 | | x^3-11x^2-186x+1080=0 | | x^3-4x^2-6=0 | | 3a+10=8 | | 5u+6v=2 | | 0.307/584 | | 7x^8y^6+56x^6y^5+2xy= | | 4(6+78843222567)=12244577763 | | 5x/10=6 | | -5.2+x=16.1 | | 8(x-7)=-104 | | 3(2r+5)+r=2(3-r)+33 | | 5a+2a-6=a+10-2 | | a=h/n | | 15/100=x/85 | | 3/x=5/(x+2) |

Equations solver categories