x^2-10x-18.75=0

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Solution for x^2-10x-18.75=0 equation:


Simplifying
x2 + -10x + -18.75 = 0

Reorder the terms:
-18.75 + -10x + x2 = 0

Solving
-18.75 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + -10x + 18.75 + x2 = 0 + 18.75

Reorder the terms:
-18.75 + 18.75 + -10x + x2 = 0 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + -10x + x2 = 0 + 18.75
-10x + x2 = 0 + 18.75

Combine like terms: 0 + 18.75 = 18.75
-10x + x2 = 18.75

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 18.75 + 25

Reorder the terms:
25 + -10x + x2 = 18.75 + 25

Combine like terms: 18.75 + 25 = 43.75
25 + -10x + x2 = 43.75

Factor a perfect square on the left side:
(x + -5)(x + -5) = 43.75

Calculate the square root of the right side: 6.614378278

Break this problem into two subproblems by setting 
(x + -5) equal to 6.614378278 and -6.614378278.

Subproblem 1

x + -5 = 6.614378278 Simplifying x + -5 = 6.614378278 Reorder the terms: -5 + x = 6.614378278 Solving -5 + x = 6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.614378278 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.614378278 + 5 x = 6.614378278 + 5 Combine like terms: 6.614378278 + 5 = 11.614378278 x = 11.614378278 Simplifying x = 11.614378278

Subproblem 2

x + -5 = -6.614378278 Simplifying x + -5 = -6.614378278 Reorder the terms: -5 + x = -6.614378278 Solving -5 + x = -6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.614378278 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.614378278 + 5 x = -6.614378278 + 5 Combine like terms: -6.614378278 + 5 = -1.614378278 x = -1.614378278 Simplifying x = -1.614378278

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.614378278, -1.614378278}

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