x*(x-38)=90

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Solution for x*(x-38)=90 equation:


Simplifying
x(x + -38) = 90

Reorder the terms:
x(-38 + x) = 90
(-38 * x + x * x) = 90
(-38x + x2) = 90

Solving
-38x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -38x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -38x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -38x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -38x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -38x + x2 = 0 + 90
-38x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-38x + x2 = 90

The x term is -38x.  Take half its coefficient (-19).
Square it (361) and add it to both sides.

Add '361' to each side of the equation.
-38x + 361 + x2 = 90 + 361

Reorder the terms:
361 + -38x + x2 = 90 + 361

Combine like terms: 90 + 361 = 451
361 + -38x + x2 = 451

Factor a perfect square on the left side:
(x + -19)(x + -19) = 451

Calculate the square root of the right side: 21.236760582

Break this problem into two subproblems by setting 
(x + -19) equal to 21.236760582 and -21.236760582.

Subproblem 1

x + -19 = 21.236760582 Simplifying x + -19 = 21.236760582 Reorder the terms: -19 + x = 21.236760582 Solving -19 + x = 21.236760582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 21.236760582 + 19 Combine like terms: -19 + 19 = 0 0 + x = 21.236760582 + 19 x = 21.236760582 + 19 Combine like terms: 21.236760582 + 19 = 40.236760582 x = 40.236760582 Simplifying x = 40.236760582

Subproblem 2

x + -19 = -21.236760582 Simplifying x + -19 = -21.236760582 Reorder the terms: -19 + x = -21.236760582 Solving -19 + x = -21.236760582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -21.236760582 + 19 Combine like terms: -19 + 19 = 0 0 + x = -21.236760582 + 19 x = -21.236760582 + 19 Combine like terms: -21.236760582 + 19 = -2.236760582 x = -2.236760582 Simplifying x = -2.236760582

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.236760582, -2.236760582}

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