x^2-10.5x+20=0

Simple and best practice solution for x^2-10.5x+20=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 x^2-10.5x+20=0 equation: 


Simplifying
x2 + -10.5x + 20 = 0

Reorder the terms:
20 + -10.5x + x2 = 0

Solving
20 + -10.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10.5x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -10.5x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10.5x + x2 = 0 + -20
-10.5x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10.5x + x2 = -20

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -20 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -20 + 27.5625

Combine like terms: -20 + 27.5625 = 7.5625
27.5625 + -10.5x + x2 = 7.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + -5.25) equal to 2.75 and -2.75.


Subproblem 1
x + -5.25 = 2.75

Simplifying
x + -5.25 = 2.75

Reorder the terms:
-5.25 + x = 2.75

Solving
-5.25 + x = 2.75

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = 2.75 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = 2.75 + 5.25
x = 2.75 + 5.25

Combine like terms: 2.75 + 5.25 = 8
x = 8

Simplifying
x = 8


Subproblem 2
x + -5.25 = -2.75

Simplifying
x + -5.25 = -2.75

Reorder the terms:
-5.25 + x = -2.75

Solving
-5.25 + x = -2.75

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = -2.75 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = -2.75 + 5.25
x = -2.75 + 5.25

Combine like terms: -2.75 + 5.25 = 2.5
x = 2.5

Simplifying
x = 2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8, 2.5}

See similar equations:

| 7a-5=-152 | | 13X+7=7X-5 | | -11.4y+5.4y=48 | | 6r-9=237 | | 6.5-4.3=210.2 | | 6=-2+2v | | 2x+6x-6=30 | | 8s^2+6s-9= | | 2x^3-12x^2+30x+200=0 | | -13=3v-7 | | x+(-15)=-29 | | 9cos(2x)=4 | | X+42=98-9x | | 2x-6-6x=30 | | 11z+10z+z=12 | | 2(x-20)=286 | | 7r-3=-185 | | 6+4y=2y | | -7-8d=7 | | 45+15=x(3+x) | | x/5-3/5 | | 10+x+2x=40 | | 2t-7=27 | | 2y^2-1=149 | | 4(x-20)=286 | | m(x)=7220+50x | | 7+49=7(x+7) | | 5a+3=-92 | | (3x+3)=45 | | 96x+2=3-80 | | 3x^2-38x-59=0 | | 5x+8+6x=63 |

Equations solver categories