3x^2=20x-7

Simple and best practice solution for 3x^2=20x-7 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=20x-7 equation: 


Simplifying
3x2 = 20x + -7

Reorder the terms:
3x2 = -7 + 20x

Solving
3x2 = -7 + 20x

Solving for variable 'x'.

Reorder the terms:
7 + -20x + 3x2 = -7 + 20x + 7 + -20x

Reorder the terms:
7 + -20x + 3x2 = -7 + 7 + 20x + -20x

Combine like terms: -7 + 7 = 0
7 + -20x + 3x2 = 0 + 20x + -20x
7 + -20x + 3x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
7 + -20x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -6.666666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -6.666666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -2.333333333
-6.666666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-6.666666667x + x2 = -2.333333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -2.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -2.333333333 + 11.11111112

Combine like terms: -2.333333333 + 11.11111112 = 8.777777787
11.11111112 + -6.666666667x + x2 = 8.777777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 8.777777787

Calculate the square root of the right side: 2.962731474

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.962731474 and -2.962731474.


Subproblem 1
x + -3.333333334 = 2.962731474

Simplifying
x + -3.333333334 = 2.962731474

Reorder the terms:
-3.333333334 + x = 2.962731474

Solving
-3.333333334 + x = 2.962731474

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 2.962731474 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 2.962731474 + 3.333333334
x = 2.962731474 + 3.333333334

Combine like terms: 2.962731474 + 3.333333334 = 6.296064808
x = 6.296064808

Simplifying
x = 6.296064808


Subproblem 2
x + -3.333333334 = -2.962731474

Simplifying
x + -3.333333334 = -2.962731474

Reorder the terms:
-3.333333334 + x = -2.962731474

Solving
-3.333333334 + x = -2.962731474

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -2.962731474 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -2.962731474 + 3.333333334
x = -2.962731474 + 3.333333334

Combine like terms: -2.962731474 + 3.333333334 = 0.37060186
x = 0.37060186

Simplifying
x = 0.37060186


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.296064808, 0.37060186}

See similar equations:

| x+3=-12 | | 3x*18=28 | | 2t+3=11 | | 4x^2+13=0 | | 5X+5=2x+53 | | 23x-56-45=0 | | 20x-2=36+2 | | 2(x-5)=(-5x)-8 | | 4y=88 | | 3t^2-36t+96=0 | | -4(6y+8)= | | x^2+5x=2x+8 | | -(4y-6)+9= | | 9-3x-6-3x=5 | | 23x=33 | | 4(y-9)=-5y-18 | | r-3=21 | | -12=-2+5v | | 11(7a)= | | 78=-29(m+3)+m | | x+2(2x+0.16)+(x+0.06)=1.4 | | 2(4x+1)=5x-9x | | (20-11)x(14+4)= | | -9x=x-8 | | 18x-3=13x-28 | | -5x+15=5x-15 | | 5x+3=8x-12 | | -0.6x+3.21=-0.8x+1.41 | | -5x-5x=56-6 | | -9y-3=-8y-5 | | (a+2)(a^2-4a+4)= | | 13x-6=7x+6 |

Equations solver categories