(x-15)(x-15)=28

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Solution for (x-15)(x-15)=28 equation:


Simplifying
(x + -15)(x + -15) = 28

Reorder the terms:
(-15 + x)(x + -15) = 28

Reorder the terms:
(-15 + x)(-15 + x) = 28

Multiply (-15 + x) * (-15 + x)
(-15(-15 + x) + x(-15 + x)) = 28
((-15 * -15 + x * -15) + x(-15 + x)) = 28
((225 + -15x) + x(-15 + x)) = 28
(225 + -15x + (-15 * x + x * x)) = 28
(225 + -15x + (-15x + x2)) = 28

Combine like terms: -15x + -15x = -30x
(225 + -30x + x2) = 28

Solving
225 + -30x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
225 + -28 + -30x + x2 = 28 + -28

Combine like terms: 225 + -28 = 197
197 + -30x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
197 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-197' to each side of the equation.
197 + -30x + -197 + x2 = 0 + -197

Reorder the terms:
197 + -197 + -30x + x2 = 0 + -197

Combine like terms: 197 + -197 = 0
0 + -30x + x2 = 0 + -197
-30x + x2 = 0 + -197

Combine like terms: 0 + -197 = -197
-30x + x2 = -197

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -197 + 225

Reorder the terms:
225 + -30x + x2 = -197 + 225

Combine like terms: -197 + 225 = 28
225 + -30x + x2 = 28

Factor a perfect square on the left side:
(x + -15)(x + -15) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -15) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + -15 = 5.291502622 Simplifying x + -15 = 5.291502622 Reorder the terms: -15 + x = 5.291502622 Solving -15 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 5.291502622 + 15 Combine like terms: -15 + 15 = 0 0 + x = 5.291502622 + 15 x = 5.291502622 + 15 Combine like terms: 5.291502622 + 15 = 20.291502622 x = 20.291502622 Simplifying x = 20.291502622

Subproblem 2

x + -15 = -5.291502622 Simplifying x + -15 = -5.291502622 Reorder the terms: -15 + x = -5.291502622 Solving -15 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -5.291502622 + 15 Combine like terms: -15 + 15 = 0 0 + x = -5.291502622 + 15 x = -5.291502622 + 15 Combine like terms: -5.291502622 + 15 = 9.708497378 x = 9.708497378 Simplifying x = 9.708497378

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.291502622, 9.708497378}

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