x(x-.03)=59.521

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Solution for x(x-.03)=59.521 equation: 


Simplifying
x(x + -0.03) = 59.521

Reorder the terms:
x(-0.03 + x) = 59.521
(-0.03 * x + x * x) = 59.521
(-0.03x + x2) = 59.521

Solving
-0.03x + x2 = 59.521

Solving for variable 'x'.

Reorder the terms:
-59.521 + -0.03x + x2 = 59.521 + -59.521

Combine like terms: 59.521 + -59.521 = 0.000
-59.521 + -0.03x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '59.521' to each side of the equation.
-59.521 + -0.03x + 59.521 + x2 = 0.000 + 59.521

Reorder the terms:
-59.521 + 59.521 + -0.03x + x2 = 0.000 + 59.521

Combine like terms: -59.521 + 59.521 = 0.000
0.000 + -0.03x + x2 = 0.000 + 59.521
-0.03x + x2 = 0.000 + 59.521

Combine like terms: 0.000 + 59.521 = 59.521
-0.03x + x2 = 59.521

The x term is -0.03x.  Take half its coefficient (-0.015).
Square it (0.000225) and add it to both sides.

Add '0.000225' to each side of the equation.
-0.03x + 0.000225 + x2 = 59.521 + 0.000225

Reorder the terms:
0.000225 + -0.03x + x2 = 59.521 + 0.000225

Combine like terms: 59.521 + 0.000225 = 59.521225
0.000225 + -0.03x + x2 = 59.521225

Factor a perfect square on the left side:
(x + -0.015)(x + -0.015) = 59.521225

Calculate the square root of the right side: 7.715

Break this problem into two subproblems by setting 
(x + -0.015) equal to 7.715 and -7.715.


Subproblem 1
x + -0.015 = 7.715

Simplifying
x + -0.015 = 7.715

Reorder the terms:
-0.015 + x = 7.715

Solving
-0.015 + x = 7.715

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.015' to each side of the equation.
-0.015 + 0.015 + x = 7.715 + 0.015

Combine like terms: -0.015 + 0.015 = 0.000
0.000 + x = 7.715 + 0.015
x = 7.715 + 0.015

Combine like terms: 7.715 + 0.015 = 7.73
x = 7.73

Simplifying
x = 7.73


Subproblem 2
x + -0.015 = -7.715

Simplifying
x + -0.015 = -7.715

Reorder the terms:
-0.015 + x = -7.715

Solving
-0.015 + x = -7.715

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.015' to each side of the equation.
-0.015 + 0.015 + x = -7.715 + 0.015

Combine like terms: -0.015 + 0.015 = 0.000
0.000 + x = -7.715 + 0.015
x = -7.715 + 0.015

Combine like terms: -7.715 + 0.015 = -7.7
x = -7.7

Simplifying
x = -7.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.73, -7.7}

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