x*(x+24)=90

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Solution for x*(x+24)=90 equation:


Simplifying
x(x + 24) = 90

Reorder the terms:
x(24 + x) = 90
(24 * x + x * x) = 90
(24x + x2) = 90

Solving
24x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 24x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 24x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 24x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 24x + x2 = 0 + 90
24x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
24x + x2 = 90

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 90 + 144

Reorder the terms:
144 + 24x + x2 = 90 + 144

Combine like terms: 90 + 144 = 234
144 + 24x + x2 = 234

Factor a perfect square on the left side:
(x + 12)(x + 12) = 234

Calculate the square root of the right side: 15.297058541

Break this problem into two subproblems by setting 
(x + 12) equal to 15.297058541 and -15.297058541.

Subproblem 1

x + 12 = 15.297058541 Simplifying x + 12 = 15.297058541 Reorder the terms: 12 + x = 15.297058541 Solving 12 + x = 15.297058541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 15.297058541 + -12 Combine like terms: 12 + -12 = 0 0 + x = 15.297058541 + -12 x = 15.297058541 + -12 Combine like terms: 15.297058541 + -12 = 3.297058541 x = 3.297058541 Simplifying x = 3.297058541

Subproblem 2

x + 12 = -15.297058541 Simplifying x + 12 = -15.297058541 Reorder the terms: 12 + x = -15.297058541 Solving 12 + x = -15.297058541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -15.297058541 + -12 Combine like terms: 12 + -12 = 0 0 + x = -15.297058541 + -12 x = -15.297058541 + -12 Combine like terms: -15.297058541 + -12 = -27.297058541 x = -27.297058541 Simplifying x = -27.297058541

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.297058541, -27.297058541}

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