x^2-14-15x=

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Solution for x^2-14-15x= equation:


Simplifying
x2 + -14 + -15x = 0

Reorder the terms:
-14 + -15x + x2 = 0

Solving
-14 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -15x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -15x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -15x + x2 = 0 + 14
-15x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-15x + x2 = 14

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 = 14 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 14 + 56.25

Combine like terms: 14 + 56.25 = 70.25
56.25 + -15x + x2 = 70.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + -7.5) equal to 8.381527307 and -8.381527307.

Subproblem 1

x + -7.5 = 8.381527307 Simplifying x + -7.5 = 8.381527307 Reorder the terms: -7.5 + x = 8.381527307 Solving -7.5 + x = 8.381527307 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 = 8.381527307 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.381527307 + 7.5 x = 8.381527307 + 7.5 Combine like terms: 8.381527307 + 7.5 = 15.881527307 x = 15.881527307 Simplifying x = 15.881527307

Subproblem 2

x + -7.5 = -8.381527307 Simplifying x + -7.5 = -8.381527307 Reorder the terms: -7.5 + x = -8.381527307 Solving -7.5 + x = -8.381527307 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 = -8.381527307 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.381527307 + 7.5 x = -8.381527307 + 7.5 Combine like terms: -8.381527307 + 7.5 = -0.881527307 x = -0.881527307 Simplifying x = -0.881527307

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.881527307, -0.881527307}

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