-x^2+84x=16

Simple and best practice solution for -x^2+84x=16 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+84x=16 equation:


Simplifying
-1x2 + 84x = 16

Reorder the terms:
84x + -1x2 = 16

Solving
84x + -1x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 84x + -1x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 84x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
16 + -84x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -84x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -84x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -84x + x2 = 0 + -16
-84x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-84x + x2 = -16

The x term is -84x.  Take half its coefficient (-42).
Square it (1764) and add it to both sides.

Add '1764' to each side of the equation.
-84x + 1764 + x2 = -16 + 1764

Reorder the terms:
1764 + -84x + x2 = -16 + 1764

Combine like terms: -16 + 1764 = 1748
1764 + -84x + x2 = 1748

Factor a perfect square on the left side:
(x + -42)(x + -42) = 1748

Calculate the square root of the right side: 41.809089921

Break this problem into two subproblems by setting 
(x + -42) equal to 41.809089921 and -41.809089921.

Subproblem 1

x + -42 = 41.809089921 Simplifying x + -42 = 41.809089921 Reorder the terms: -42 + x = 41.809089921 Solving -42 + x = 41.809089921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = 41.809089921 + 42 Combine like terms: -42 + 42 = 0 0 + x = 41.809089921 + 42 x = 41.809089921 + 42 Combine like terms: 41.809089921 + 42 = 83.809089921 x = 83.809089921 Simplifying x = 83.809089921

Subproblem 2

x + -42 = -41.809089921 Simplifying x + -42 = -41.809089921 Reorder the terms: -42 + x = -41.809089921 Solving -42 + x = -41.809089921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = -41.809089921 + 42 Combine like terms: -42 + 42 = 0 0 + x = -41.809089921 + 42 x = -41.809089921 + 42 Combine like terms: -41.809089921 + 42 = 0.190910079 x = 0.190910079 Simplifying x = 0.190910079

Solution

The solution to the problem is based on the solutions from the subproblems. x = {83.809089921, 0.190910079}

See similar equations:

| 6x=16n | | 4e^2x+1=8 | | 16x=6n | | -x^2+bx-16=84 | | -x^2+84x-16=0 | | 18n+12=27+3 | | 15-25=9m+17 | | 9p-3(8-p)= | | 2x+8=67 | | X-7=3x+5 | | 3(x+4)-5=2(3x-2)+2 | | 4x+3yx-4y=342 | | (n+4)*8=72 | | (n-4)*5=30 | | (n+2)*6=30 | | 4x+3yx-4y= | | 5x-4=108-9x | | 10+4x=74 | | ((-6x^2)+18x+60)=0 | | 14-x=12 | | Kx^2-2kx+2=0 | | 2x+(x-4)-4x= | | 2x^2=17x+42 | | x-3=3(3x-392+30*2)-17(2x) | | .25q+.05q=3 | | 3x-12y=o | | 2x^3-3x+6x^5-9=0 | | -48-10=8x-6x | | 4h^2-2h+1=7 | | X^2-9+20= | | 9x^2+6x=-16 | | 25q+5q+45=345 |

Equations solver categories