x*x-9x+15=0

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Solution for x*x-9x+15=0 equation:


Simplifying
x * x + -9x + 15 = 0

Multiply x * x
x2 + -9x + 15 = 0

Reorder the terms:
15 + -9x + x2 = 0

Solving
15 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -9x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -9x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -9x + x2 = 0 + -15
-9x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-9x + x2 = -15

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -15 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -15 + 20.25

Combine like terms: -15 + 20.25 = 5.25
20.25 + -9x + x2 = 5.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -4.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + -4.5 = 2.291287847 Simplifying x + -4.5 = 2.291287847 Reorder the terms: -4.5 + x = 2.291287847 Solving -4.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.291287847 + 4.5 x = 2.291287847 + 4.5 Combine like terms: 2.291287847 + 4.5 = 6.791287847 x = 6.791287847 Simplifying x = 6.791287847

Subproblem 2

x + -4.5 = -2.291287847 Simplifying x + -4.5 = -2.291287847 Reorder the terms: -4.5 + x = -2.291287847 Solving -4.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.291287847 + 4.5 x = -2.291287847 + 4.5 Combine like terms: -2.291287847 + 4.5 = 2.208712153 x = 2.208712153 Simplifying x = 2.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.791287847, 2.208712153}

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