x^2-30x+54=50

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Solution for x^2-30x+54=50 equation:


Simplifying
x2 + -30x + 54 = 50

Reorder the terms:
54 + -30x + x2 = 50

Solving
54 + -30x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
54 + -50 + -30x + x2 = 50 + -50

Combine like terms: 54 + -50 = 4
4 + -30x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
4 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -30x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -30x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -30x + x2 = 0 + -4
-30x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-30x + x2 = -4

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 = -4 + 225

Reorder the terms:
225 + -30x + x2 = -4 + 225

Combine like terms: -4 + 225 = 221
225 + -30x + x2 = 221

Factor a perfect square on the left side:
(x + -15)(x + -15) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(x + -15) equal to 14.866068747 and -14.866068747.

Subproblem 1

x + -15 = 14.866068747 Simplifying x + -15 = 14.866068747 Reorder the terms: -15 + x = 14.866068747 Solving -15 + x = 14.866068747 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 = 14.866068747 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.866068747 + 15 x = 14.866068747 + 15 Combine like terms: 14.866068747 + 15 = 29.866068747 x = 29.866068747 Simplifying x = 29.866068747

Subproblem 2

x + -15 = -14.866068747 Simplifying x + -15 = -14.866068747 Reorder the terms: -15 + x = -14.866068747 Solving -15 + x = -14.866068747 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 = -14.866068747 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.866068747 + 15 x = -14.866068747 + 15 Combine like terms: -14.866068747 + 15 = 0.133931253 x = 0.133931253 Simplifying x = 0.133931253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.866068747, 0.133931253}

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