x^2-15x+16=0

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Solution for x^2-15x+16=0 equation:


Simplifying
x2 + -15x + 16 = 0

Reorder the terms:
16 + -15x + x2 = 0

Solving
16 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -15x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -15x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -15x + x2 = 0 + -16
-15x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-15x + x2 = -16

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -16 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -16 + 56.25

Combine like terms: -16 + 56.25 = 40.25
56.25 + -15x + x2 = 40.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -7.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

x + -7.5 = 6.34428877 Simplifying x + -7.5 = 6.34428877 Reorder the terms: -7.5 + x = 6.34428877 Solving -7.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.34428877 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.34428877 + 7.5 x = 6.34428877 + 7.5 Combine like terms: 6.34428877 + 7.5 = 13.84428877 x = 13.84428877 Simplifying x = 13.84428877

Subproblem 2

x + -7.5 = -6.34428877 Simplifying x + -7.5 = -6.34428877 Reorder the terms: -7.5 + x = -6.34428877 Solving -7.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.34428877 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.34428877 + 7.5 x = -6.34428877 + 7.5 Combine like terms: -6.34428877 + 7.5 = 1.15571123 x = 1.15571123 Simplifying x = 1.15571123

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.84428877, 1.15571123}

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