x^2-17x-48=0

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Solution for x^2-17x-48=0 equation:


Simplifying
x2 + -17x + -48 = 0

Reorder the terms:
-48 + -17x + x2 = 0

Solving
-48 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -17x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -17x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -17x + x2 = 0 + 48
-17x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-17x + x2 = 48

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = 48 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 48 + 72.25

Combine like terms: 48 + 72.25 = 120.25
72.25 + -17x + x2 = 120.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + -8.5) equal to 10.9658561 and -10.9658561.

Subproblem 1

x + -8.5 = 10.9658561 Simplifying x + -8.5 = 10.9658561 Reorder the terms: -8.5 + x = 10.9658561 Solving -8.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 10.9658561 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 10.9658561 + 8.5 x = 10.9658561 + 8.5 Combine like terms: 10.9658561 + 8.5 = 19.4658561 x = 19.4658561 Simplifying x = 19.4658561

Subproblem 2

x + -8.5 = -10.9658561 Simplifying x + -8.5 = -10.9658561 Reorder the terms: -8.5 + x = -10.9658561 Solving -8.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -10.9658561 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -10.9658561 + 8.5 x = -10.9658561 + 8.5 Combine like terms: -10.9658561 + 8.5 = -2.4658561 x = -2.4658561 Simplifying x = -2.4658561

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.4658561, -2.4658561}

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