4x^2+32x+6-3x^2-7x+10=0

Simple and best practice solution for 4x^2+32x+6-3x^2-7x+10=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 4x^2+32x+6-3x^2-7x+10=0 equation:


Simplifying
4x2 + 32x + 6 + -3x2 + -7x + 10 = 0

Reorder the terms:
6 + 10 + 32x + -7x + 4x2 + -3x2 = 0

Combine like terms: 6 + 10 = 16
16 + 32x + -7x + 4x2 + -3x2 = 0

Combine like terms: 32x + -7x = 25x
16 + 25x + 4x2 + -3x2 = 0

Combine like terms: 4x2 + -3x2 = 1x2
16 + 25x + 1x2 = 0

Solving
16 + 25x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 25x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 25x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 25x + x2 = 0 + -16
25x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
25x + x2 = -16

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -16 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -16 + 156.25

Combine like terms: -16 + 156.25 = 140.25
156.25 + 25x + x2 = 140.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 140.25

Calculate the square root of the right side: 11.842719282

Break this problem into two subproblems by setting 
(x + 12.5) equal to 11.842719282 and -11.842719282.

Subproblem 1

x + 12.5 = 11.842719282 Simplifying x + 12.5 = 11.842719282 Reorder the terms: 12.5 + x = 11.842719282 Solving 12.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 11.842719282 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 11.842719282 + -12.5 x = 11.842719282 + -12.5 Combine like terms: 11.842719282 + -12.5 = -0.657280718 x = -0.657280718 Simplifying x = -0.657280718

Subproblem 2

x + 12.5 = -11.842719282 Simplifying x + 12.5 = -11.842719282 Reorder the terms: 12.5 + x = -11.842719282 Solving 12.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -11.842719282 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -11.842719282 + -12.5 x = -11.842719282 + -12.5 Combine like terms: -11.842719282 + -12.5 = -24.342719282 x = -24.342719282 Simplifying x = -24.342719282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.657280718, -24.342719282}

See similar equations:

| 19(j+18)=646 | | 4x-3=-12-4x | | 4x^2+32x+6+3x^2-7x+10=0 | | 2x-(6-x)=3x+2(x-8) | | 2(4x-7)(7x+5)=0 | | 2x-5(x-5)=-4+5x-27 | | 4x^2-5=64 | | 13-9x=-35 | | 4x-80=320 | | 2x-37=20+5x | | 2x+5y=600 | | 4x+48=8(x+4) | | 3x=0.75x+5 | | 0.75a=-8 | | 5x-2y=187 | | 40=4(s+10) | | -(h+3.6)=-5.1 | | 5x-75=125 | | 2(2r-7)-9= | | 3b-2=5b+4 | | -6(x+4)=8x-10 | | 0.3=(1+0.23*x*30) | | 4=X^2+X | | Xdy-y+xy^3(1+Lynx)dx=0 | | 2ln(x)-ln(2x-3)=ln(5x)-ln(x+2) | | 3a-1=-15 | | 11.3=5.5+-m | | 3v+11=5(v+1) | | 2(5x-1)-9(x-1)= | | 8x-120=120 | | log^3(x-15)=4 | | (5/6)x=(4/5) |

Equations solver categories