0=x^2-17x-225

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Solution for 0=x^2-17x-225 equation:


Simplifying
0 = x2 + -17x + -225

Reorder the terms:
0 = -225 + -17x + x2

Solving
0 = -225 + -17x + x2

Solving for variable 'x'.

Combine like terms: 0 + 225 = 225
225 + 17x + -1x2 = -225 + -17x + x2 + 225 + 17x + -1x2

Reorder the terms:
225 + 17x + -1x2 = -225 + 225 + -17x + 17x + x2 + -1x2

Combine like terms: -225 + 225 = 0
225 + 17x + -1x2 = 0 + -17x + 17x + x2 + -1x2
225 + 17x + -1x2 = -17x + 17x + x2 + -1x2

Combine like terms: -17x + 17x = 0
225 + 17x + -1x2 = 0 + x2 + -1x2
225 + 17x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
225 + 17x + -1x2 = 0

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

Divide each side by '-1'.
-225 + -17x + x2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -17x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -17x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -17x + x2 = 0 + 225
-17x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-17x + x2 = 225

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 = 225 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 225 + 72.25

Combine like terms: 225 + 72.25 = 297.25
72.25 + -17x + x2 = 297.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 297.25

Calculate the square root of the right side: 17.24093965

Break this problem into two subproblems by setting 
(x + -8.5) equal to 17.24093965 and -17.24093965.

Subproblem 1

x + -8.5 = 17.24093965 Simplifying x + -8.5 = 17.24093965 Reorder the terms: -8.5 + x = 17.24093965 Solving -8.5 + x = 17.24093965 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 = 17.24093965 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 17.24093965 + 8.5 x = 17.24093965 + 8.5 Combine like terms: 17.24093965 + 8.5 = 25.74093965 x = 25.74093965 Simplifying x = 25.74093965

Subproblem 2

x + -8.5 = -17.24093965 Simplifying x + -8.5 = -17.24093965 Reorder the terms: -8.5 + x = -17.24093965 Solving -8.5 + x = -17.24093965 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 = -17.24093965 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -17.24093965 + 8.5 x = -17.24093965 + 8.5 Combine like terms: -17.24093965 + 8.5 = -8.74093965 x = -8.74093965 Simplifying x = -8.74093965

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.74093965, -8.74093965}

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