x^2-14x+22.5=0

Simple and best practice solution for x^2-14x+22.5=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^2-14x+22.5=0 equation: 


Simplifying
x2 + -14x + 22.5 = 0

Reorder the terms:
22.5 + -14x + x2 = 0

Solving
22.5 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-22.5' to each side of the equation.
22.5 + -14x + -22.5 + x2 = 0 + -22.5

Reorder the terms:
22.5 + -22.5 + -14x + x2 = 0 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + -14x + x2 = 0 + -22.5
-14x + x2 = 0 + -22.5

Combine like terms: 0 + -22.5 = -22.5
-14x + x2 = -22.5

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -22.5 + 49

Reorder the terms:
49 + -14x + x2 = -22.5 + 49

Combine like terms: -22.5 + 49 = 26.5
49 + -14x + x2 = 26.5

Factor a perfect square on the left side:
(x + -7)(x + -7) = 26.5

Calculate the square root of the right side: 5.14781507

Break this problem into two subproblems by setting 
(x + -7) equal to 5.14781507 and -5.14781507.


Subproblem 1
x + -7 = 5.14781507

Simplifying
x + -7 = 5.14781507

Reorder the terms:
-7 + x = 5.14781507

Solving
-7 + x = 5.14781507

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 5.14781507 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.14781507 + 7
x = 5.14781507 + 7

Combine like terms: 5.14781507 + 7 = 12.14781507
x = 12.14781507

Simplifying
x = 12.14781507


Subproblem 2
x + -7 = -5.14781507

Simplifying
x + -7 = -5.14781507

Reorder the terms:
-7 + x = -5.14781507

Solving
-7 + x = -5.14781507

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -5.14781507 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.14781507 + 7
x = -5.14781507 + 7

Combine like terms: -5.14781507 + 7 = 1.85218493
x = 1.85218493

Simplifying
x = 1.85218493


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.14781507, 1.85218493}

See similar equations:

| -3+7+(-8)= | | x^2+19x-106=0 | | -h/3-4=23 | | 7x+9x-46=115-7x | | 2.5x-4=1.5x | | -3+7+(8)= | | X+2/3=27/8 | | -9x-3=-4-3 | | -7+21=-4 | | 0.1y+x=18 | | 3w=3/73/1 | | 8-(-9)-7+2= | | 2x^2+14x-22.5=0 | | 5x+8x-88=44-9x | | 11/2+m/-2=31/2 | | x^2=6x+14 | | q/-7=4 | | 5(-9x-4)-5x=-3 | | 2x-(3x-2)+5=17 | | M+1/6=5/6 | | k-69=-55 | | -7+3(-7x+5)=-5 | | 2x-8x+48=3x+39 | | 3h=90 | | -4x-5=-x+4 | | 70=y+2x | | j-54=-17 | | h/12-5=-20 | | 5m-2m+10= | | x/12+7=-2 | | 10=h/7 | | 70=2x+y |

Equations solver categories