3x^2+14x+10=8

Simple and best practice solution for 3x^2+14x+10=8 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 3x^2+14x+10=8 equation:


Simplifying
3x2 + 14x + 10 = 8

Reorder the terms:
10 + 14x + 3x2 = 8

Solving
10 + 14x + 3x2 = 8

Solving for variable 'x'.

Reorder the terms:
10 + -8 + 14x + 3x2 = 8 + -8

Combine like terms: 10 + -8 = 2
2 + 14x + 3x2 = 8 + -8

Combine like terms: 8 + -8 = 0
2 + 14x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 4.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 4.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 4.666666667x + x2 = 0 + -0.6666666667
4.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
4.666666667x + x2 = -0.6666666667

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = -0.6666666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -0.6666666667 + 5.444444448

Combine like terms: -0.6666666667 + 5.444444448 = 4.7777777813
5.444444448 + 4.666666667x + x2 = 4.7777777813

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 4.7777777813

Calculate the square root of the right side: 2.185812842

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.185812842 and -2.185812842.


Subproblem 1
x + 2.333333334 = 2.185812842

Simplifying
x + 2.333333334 = 2.185812842

Reorder the terms:
2.333333334 + x = 2.185812842

Solving
2.333333334 + x = 2.185812842

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 2.185812842 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.185812842 + -2.333333334
x = 2.185812842 + -2.333333334

Combine like terms: 2.185812842 + -2.333333334 = -0.147520492
x = -0.147520492

Simplifying
x = -0.147520492


Subproblem 2
x + 2.333333334 = -2.185812842

Simplifying
x + 2.333333334 = -2.185812842

Reorder the terms:
2.333333334 + x = -2.185812842

Solving
2.333333334 + x = -2.185812842

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -2.185812842 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.185812842 + -2.333333334
x = -2.185812842 + -2.333333334

Combine like terms: -2.185812842 + -2.333333334 = -4.519146176
x = -4.519146176

Simplifying
x = -4.519146176


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.147520492, -4.519146176}

See similar equations:

| -188=-3x-7(2x+5) | | 17x/4-3x=10 | | 426/7u | | 30bc/12b^2 | | 36-8p=-5(2p-6) | | 6(1/27)^4/x=18 | | 12x-4=2x+32 | | 2(x+4)+1-5x=(3-1-x)+7 | | -3(6+8a)=33-7a | | 5(x+3)+x=4(x-3)+3 | | 2x+78=11x-48 | | 5x/y^2*2y/7x | | 36xy+6x+6y+1=143 | | =(e^5x)*(e^10x) | | 3y-x+9=0 | | (x^6+16x^3+64)(x^3+8)=0 | | k=18-x^2-2 | | 4x-6=-2x-1 | | 226-u=287 | | 41-6x=14-9x | | -(x+m)=3(x+9)-10 | | 170=32-y | | 8(0)-2y=-8 | | (-36x^2)+(96x)-36=0 | | 3=w+8 | | 7x^2(8x^2y^3-8xz^4y+4y^3z)= | | 41-8x=49-2x | | (3y-1)(4+y)=0 | | 6+4x=-6+x | | 8x-2(0)=-8 | | 3(2a-4)=24 | | (x-3)(x+3)+10=4x |

Equations solver categories