x^2-14x-53=0

Simple and best practice solution for x^2-14x-53=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-53=0 equation: 


Simplifying
x2 + -14x + -53 = 0

Reorder the terms:
-53 + -14x + x2 = 0

Solving
-53 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '53' to each side of the equation.
-53 + -14x + 53 + x2 = 0 + 53

Reorder the terms:
-53 + 53 + -14x + x2 = 0 + 53

Combine like terms: -53 + 53 = 0
0 + -14x + x2 = 0 + 53
-14x + x2 = 0 + 53

Combine like terms: 0 + 53 = 53
-14x + x2 = 53

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 = 53 + 49

Reorder the terms:
49 + -14x + x2 = 53 + 49

Combine like terms: 53 + 49 = 102
49 + -14x + x2 = 102

Factor a perfect square on the left side:
(x + -7)(x + -7) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + -7) equal to 10.099504938 and -10.099504938.


Subproblem 1
x + -7 = 10.099504938

Simplifying
x + -7 = 10.099504938

Reorder the terms:
-7 + x = 10.099504938

Solving
-7 + x = 10.099504938

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 = 10.099504938 + 7

Combine like terms: -7 + 7 = 0
0 + x = 10.099504938 + 7
x = 10.099504938 + 7

Combine like terms: 10.099504938 + 7 = 17.099504938
x = 17.099504938

Simplifying
x = 17.099504938


Subproblem 2
x + -7 = -10.099504938

Simplifying
x + -7 = -10.099504938

Reorder the terms:
-7 + x = -10.099504938

Solving
-7 + x = -10.099504938

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 = -10.099504938 + 7

Combine like terms: -7 + 7 = 0
0 + x = -10.099504938 + 7
x = -10.099504938 + 7

Combine like terms: -10.099504938 + 7 = -3.099504938
x = -3.099504938

Simplifying
x = -3.099504938


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.099504938, -3.099504938}

See similar equations:

| -3/5*-1/9 | | 2-n=-1 | | t+12=12 | | 25.56+x=25.72 | | 14-3f=2 | | x-10=3x-12 | | -2-n=0 | | 90=-2(3-6k) | | 3r+19=4-2r | | logx=0.32 | | 2(x+6)=3(x+7) | | x+1=12x-1 | | 3/5*(-1/6) | | 3r/10=6 | | -2.73+x=-.3 | | q/-5=18 | | 2log(3x+5)=4 | | -19.5=9.5x-5.5x | | 12(x+1)=-3 | | 22=x-7.8 | | 14-5x=-52 | | 121=4x+7 | | 4(x-5)=2(x+2) | | x+15+75=x | | (x-lnx*2x)/x^4 | | -3x+8x=10 | | 2n-3/7=1n-2/5 | | x+15=x+75 | | -6x+8=-3x-10 | | 6x-3x=-15 | | x^2-2x=20.085 | | 3n-6n=-12 |

Equations solver categories