x^2-6x-150=0

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Solution for x^2-6x-150=0 equation:


Simplifying
x2 + -6x + -150 = 0

Reorder the terms:
-150 + -6x + x2 = 0

Solving
-150 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + -6x + 150 + x2 = 0 + 150

Reorder the terms:
-150 + 150 + -6x + x2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + -6x + x2 = 0 + 150
-6x + x2 = 0 + 150

Combine like terms: 0 + 150 = 150
-6x + x2 = 150

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 150 + 9

Reorder the terms:
9 + -6x + x2 = 150 + 9

Combine like terms: 150 + 9 = 159
9 + -6x + x2 = 159

Factor a perfect square on the left side:
(x + -3)(x + -3) = 159

Calculate the square root of the right side: 12.609520213

Break this problem into two subproblems by setting 
(x + -3) equal to 12.609520213 and -12.609520213.

Subproblem 1

x + -3 = 12.609520213 Simplifying x + -3 = 12.609520213 Reorder the terms: -3 + x = 12.609520213 Solving -3 + x = 12.609520213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 12.609520213 + 3 Combine like terms: -3 + 3 = 0 0 + x = 12.609520213 + 3 x = 12.609520213 + 3 Combine like terms: 12.609520213 + 3 = 15.609520213 x = 15.609520213 Simplifying x = 15.609520213

Subproblem 2

x + -3 = -12.609520213 Simplifying x + -3 = -12.609520213 Reorder the terms: -3 + x = -12.609520213 Solving -3 + x = -12.609520213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -12.609520213 + 3 Combine like terms: -3 + 3 = 0 0 + x = -12.609520213 + 3 x = -12.609520213 + 3 Combine like terms: -12.609520213 + 3 = -9.609520213 x = -9.609520213 Simplifying x = -9.609520213

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.609520213, -9.609520213}

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