.5*15=x(161.25-x)

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Solution for .5*15=x(161.25-x) equation:


Simplifying
0.5 * 15 = x(161.25 + -1x)

Multiply 0.5 * 15
7.5 = x(161.25 + -1x)
7.5 = (161.25 * x + -1x * x)
7.5 = (161.25x + -1x2)

Solving
7.5 = 161.25x + -1x2

Solving for variable 'x'.

Reorder the terms:
7.5 + -161.25x + x2 = 161.25x + -161.25x + -1x2 + x2

Combine like terms: 161.25x + -161.25x = 0.00
7.5 + -161.25x + x2 = 0.00 + -1x2 + x2
7.5 + -161.25x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
7.5 + -161.25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + -161.25x + -7.5 + x2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + -161.25x + x2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + -161.25x + x2 = 0 + -7.5
-161.25x + x2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
-161.25x + x2 = -7.5

The x term is -161.25x.  Take half its coefficient (-80.625).
Square it (6500.390625) and add it to both sides.

Add '6500.390625' to each side of the equation.
-161.25x + 6500.390625 + x2 = -7.5 + 6500.390625

Reorder the terms:
6500.390625 + -161.25x + x2 = -7.5 + 6500.390625

Combine like terms: -7.5 + 6500.390625 = 6492.890625
6500.390625 + -161.25x + x2 = 6492.890625

Factor a perfect square on the left side:
(x + -80.625)(x + -80.625) = 6492.890625

Calculate the square root of the right side: 80.578474948

Break this problem into two subproblems by setting 
(x + -80.625) equal to 80.578474948 and -80.578474948.

Subproblem 1

x + -80.625 = 80.578474948 Simplifying x + -80.625 = 80.578474948 Reorder the terms: -80.625 + x = 80.578474948 Solving -80.625 + x = 80.578474948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80.625' to each side of the equation. -80.625 + 80.625 + x = 80.578474948 + 80.625 Combine like terms: -80.625 + 80.625 = 0.000 0.000 + x = 80.578474948 + 80.625 x = 80.578474948 + 80.625 Combine like terms: 80.578474948 + 80.625 = 161.203474948 x = 161.203474948 Simplifying x = 161.203474948

Subproblem 2

x + -80.625 = -80.578474948 Simplifying x + -80.625 = -80.578474948 Reorder the terms: -80.625 + x = -80.578474948 Solving -80.625 + x = -80.578474948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80.625' to each side of the equation. -80.625 + 80.625 + x = -80.578474948 + 80.625 Combine like terms: -80.625 + 80.625 = 0.000 0.000 + x = -80.578474948 + 80.625 x = -80.578474948 + 80.625 Combine like terms: -80.578474948 + 80.625 = 0.046525052 x = 0.046525052 Simplifying x = 0.046525052

Solution

The solution to the problem is based on the solutions from the subproblems. x = {161.203474948, 0.046525052}

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