x^2-x-84=0

Simple and best practice solution for x^2-x-84=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-x-84=0 equation:


Simplifying
x2 + -1x + -84 = 0

Reorder the terms:
-84 + -1x + x2 = 0

Solving
-84 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -1x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + -1x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -1x + x2 = 0 + 84
-1x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
-1x + x2 = 84

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 84 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 84 + 0.25

Combine like terms: 84 + 0.25 = 84.25
0.25 + -1x + x2 = 84.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(x + -0.5) equal to 9.178779875 and -9.178779875.

Subproblem 1

x + -0.5 = 9.178779875 Simplifying x + -0.5 = 9.178779875 Reorder the terms: -0.5 + x = 9.178779875 Solving -0.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 9.178779875 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.178779875 + 0.5 x = 9.178779875 + 0.5 Combine like terms: 9.178779875 + 0.5 = 9.678779875 x = 9.678779875 Simplifying x = 9.678779875

Subproblem 2

x + -0.5 = -9.178779875 Simplifying x + -0.5 = -9.178779875 Reorder the terms: -0.5 + x = -9.178779875 Solving -0.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -9.178779875 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.178779875 + 0.5 x = -9.178779875 + 0.5 Combine like terms: -9.178779875 + 0.5 = -8.678779875 x = -8.678779875 Simplifying x = -8.678779875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.678779875, -8.678779875}

See similar equations:

| 199-7x=29x+23 | | 73-4x=5x+24 | | 3(7+3r)=4(5+2r) | | 7-9x=192-44x | | 7x-23=33 | | 9p+17=13p+1 | | 7-7x=38-14x | | 49=11x-6 | | 13-10x=33-17x | | 2x-5=44+5x | | 5x-5x=93-3 | | (Y-5)(Y-3)=0 | | 2(x+9)-24= | | 4=3p+22 | | 7-2x=16+7x | | 149-6x=4x+9 | | (x-5)(3x+7)=0 | | 2x-4x=16 | | 9xy=10 | | 5x+10=4x+1 | | 6-30=-4x | | 4x+16-8=3x+8 | | 8x+3=2n+2 | | 4*s-12=5*s+51 | | 3+2c-2c^2= | | 94-2x=10+22 | | -8m-[2(11-2m)+4]=9m | | m-18=3(m) | | 3+2c+2c^2= | | y=1+2.5x | | 2x-4(x+1)=-(7x+8)+x | | 8ln(4x)=16 |

Equations solver categories