2x^2-16x+27=0

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Solution for 2x^2-16x+27=0 equation:


Simplifying
2x2 + -16x + 27 = 0

Reorder the terms:
27 + -16x + 2x2 = 0

Solving
27 + -16x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
13.5 + -8x + x2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -8x + -13.5 + x2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -8x + x2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -8x + x2 = 0 + -13.5
-8x + x2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-8x + x2 = -13.5

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -13.5 + 16

Reorder the terms:
16 + -8x + x2 = -13.5 + 16

Combine like terms: -13.5 + 16 = 2.5
16 + -8x + x2 = 2.5

Factor a perfect square on the left side:
(x + -4)(x + -4) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -4) equal to 1.58113883 and -1.58113883.

Subproblem 1

x + -4 = 1.58113883 Simplifying x + -4 = 1.58113883 Reorder the terms: -4 + x = 1.58113883 Solving -4 + x = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.58113883 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.58113883 + 4 x = 1.58113883 + 4 Combine like terms: 1.58113883 + 4 = 5.58113883 x = 5.58113883 Simplifying x = 5.58113883

Subproblem 2

x + -4 = -1.58113883 Simplifying x + -4 = -1.58113883 Reorder the terms: -4 + x = -1.58113883 Solving -4 + x = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.58113883 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.58113883 + 4 x = -1.58113883 + 4 Combine like terms: -1.58113883 + 4 = 2.41886117 x = 2.41886117 Simplifying x = 2.41886117

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.58113883, 2.41886117}

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