3x^2-14x+10=0

Simple and best practice solution for 3x^2-14x+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 3x^2-14x+10=0 equation: 


Simplifying
3x2 + -14x + 10 = 0

Reorder the terms:
10 + -14x + 3x2 = 0

Solving
10 + -14x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
3.333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -4.666666667x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -4.666666667x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + -3.333333333
-4.666666667x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-4.666666667x + x2 = -3.333333333

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 = -3.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -3.333333333 + 5.444444448

Combine like terms: -3.333333333 + 5.444444448 = 2.111111115
5.444444448 + -4.666666667x + x2 = 2.111111115

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 2.111111115

Calculate the square root of the right side: 1.452966316

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 1.452966316 and -1.452966316.


Subproblem 1
x + -2.333333334 = 1.452966316

Simplifying
x + -2.333333334 = 1.452966316

Reorder the terms:
-2.333333334 + x = 1.452966316

Solving
-2.333333334 + x = 1.452966316

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 = 1.452966316 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 1.452966316 + 2.333333334
x = 1.452966316 + 2.333333334

Combine like terms: 1.452966316 + 2.333333334 = 3.78629965
x = 3.78629965

Simplifying
x = 3.78629965


Subproblem 2
x + -2.333333334 = -1.452966316

Simplifying
x + -2.333333334 = -1.452966316

Reorder the terms:
-2.333333334 + x = -1.452966316

Solving
-2.333333334 + x = -1.452966316

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 = -1.452966316 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -1.452966316 + 2.333333334
x = -1.452966316 + 2.333333334

Combine like terms: -1.452966316 + 2.333333334 = 0.880367018
x = 0.880367018

Simplifying
x = 0.880367018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.78629965, 0.880367018}

See similar equations:

| 30+3y-3=11y-9-2y | | 5p+9=2p+12 | | 16x^2-24x+9=3 | | 10+5(x-4)=8x-(5x+4) | | y=3x^2-10x+2 | | x^2-8x+16=11 | | s^2=-18-11s | | -25x+12y=8 | | 3x+6x-4+5x=97-2x-6-7x | | 9p^2=-10p+1 | | 3w-4=7 | | x^2+4x+4=6 | | 6(r+2)-4=(-10) | | 2x=12-x | | 6y-15y=-32-40 | | -x+10=x+2 | | -3(2b+6)+2b=20 | | 4(8-3y)=72 | | 7x-22=2x+31 | | 2y(y+4)=42 | | -5(2w+6)=100 | | 3(2x-4)=6 | | 14t-8-11t=32 | | 7x-22=2x+33 | | 2x+10=88 | | 2x-3=-6 | | -2q-65=35 | | y=7*60-370 | | 25x+15(7x-370)-2250=0 | | 3-5n=-22 | | 13-7(x-4)=8(x-3) | | x^2-3x+27=6x+7 |

Equations solver categories