150=x^2-13x

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Solution for 150=x^2-13x equation:


Simplifying
150 = x2 + -13x

Reorder the terms:
150 = -13x + x2

Solving
150 = -13x + x2

Solving for variable 'x'.

Reorder the terms:
150 + 13x + -1x2 = -13x + 13x + x2 + -1x2

Combine like terms: -13x + 13x = 0
150 + 13x + -1x2 = 0 + x2 + -1x2
150 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
150 + 13x + -1x2 = 0

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

Divide each side by '-1'.
-150 + -13x + x2 = 0

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + -13x + 150 + x2 = 0 + 150

Reorder the terms:
-150 + 150 + -13x + x2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + -13x + x2 = 0 + 150
-13x + x2 = 0 + 150

Combine like terms: 0 + 150 = 150
-13x + x2 = 150

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 150 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 150 + 42.25

Combine like terms: 150 + 42.25 = 192.25
42.25 + -13x + x2 = 192.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 192.25

Calculate the square root of the right side: 13.865424624

Break this problem into two subproblems by setting 
(x + -6.5) equal to 13.865424624 and -13.865424624.

Subproblem 1

x + -6.5 = 13.865424624 Simplifying x + -6.5 = 13.865424624 Reorder the terms: -6.5 + x = 13.865424624 Solving -6.5 + x = 13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 13.865424624 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 13.865424624 + 6.5 x = 13.865424624 + 6.5 Combine like terms: 13.865424624 + 6.5 = 20.365424624 x = 20.365424624 Simplifying x = 20.365424624

Subproblem 2

x + -6.5 = -13.865424624 Simplifying x + -6.5 = -13.865424624 Reorder the terms: -6.5 + x = -13.865424624 Solving -6.5 + x = -13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -13.865424624 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -13.865424624 + 6.5 x = -13.865424624 + 6.5 Combine like terms: -13.865424624 + 6.5 = -7.365424624 x = -7.365424624 Simplifying x = -7.365424624

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.365424624, -7.365424624}

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