X^2-16X-87=0

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Solution for X^2-16X-87=0 equation:


Simplifying
X2 + -16X + -87 = 0

Reorder the terms:
-87 + -16X + X2 = 0

Solving
-87 + -16X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '87' to each side of the equation.
-87 + -16X + 87 + X2 = 0 + 87

Reorder the terms:
-87 + 87 + -16X + X2 = 0 + 87

Combine like terms: -87 + 87 = 0
0 + -16X + X2 = 0 + 87
-16X + X2 = 0 + 87

Combine like terms: 0 + 87 = 87
-16X + X2 = 87

The X term is -16X.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16X + 64 + X2 = 87 + 64

Reorder the terms:
64 + -16X + X2 = 87 + 64

Combine like terms: 87 + 64 = 151
64 + -16X + X2 = 151

Factor a perfect square on the left side:
(X + -8)(X + -8) = 151

Calculate the square root of the right side: 12.288205727

Break this problem into two subproblems by setting 
(X + -8) equal to 12.288205727 and -12.288205727.

Subproblem 1

X + -8 = 12.288205727 Simplifying X + -8 = 12.288205727 Reorder the terms: -8 + X = 12.288205727 Solving -8 + X = 12.288205727 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + X = 12.288205727 + 8 Combine like terms: -8 + 8 = 0 0 + X = 12.288205727 + 8 X = 12.288205727 + 8 Combine like terms: 12.288205727 + 8 = 20.288205727 X = 20.288205727 Simplifying X = 20.288205727

Subproblem 2

X + -8 = -12.288205727 Simplifying X + -8 = -12.288205727 Reorder the terms: -8 + X = -12.288205727 Solving -8 + X = -12.288205727 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + X = -12.288205727 + 8 Combine like terms: -8 + 8 = 0 0 + X = -12.288205727 + 8 X = -12.288205727 + 8 Combine like terms: -12.288205727 + 8 = -4.288205727 X = -4.288205727 Simplifying X = -4.288205727

Solution

The solution to the problem is based on the solutions from the subproblems. X = {20.288205727, -4.288205727}

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