-.05x^2+4.5x-6.5=0

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Solution for -.05x^2+4.5x-6.5=0 equation:


Simplifying
-0.05x2 + 4.5x + -6.5 = 0

Reorder the terms:
-6.5 + 4.5x + -0.05x2 = 0

Solving
-6.5 + 4.5x + -0.05x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
130 + -90x + x2 = 0

Move the constant term to the right:

Add '-130' to each side of the equation.
130 + -90x + -130 + x2 = 0 + -130

Reorder the terms:
130 + -130 + -90x + x2 = 0 + -130

Combine like terms: 130 + -130 = 0
0 + -90x + x2 = 0 + -130
-90x + x2 = 0 + -130

Combine like terms: 0 + -130 = -130
-90x + x2 = -130

The x term is -90x.  Take half its coefficient (-45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
-90x + 2025 + x2 = -130 + 2025

Reorder the terms:
2025 + -90x + x2 = -130 + 2025

Combine like terms: -130 + 2025 = 1895
2025 + -90x + x2 = 1895

Factor a perfect square on the left side:
(x + -45)(x + -45) = 1895

Calculate the square root of the right side: 43.531597719

Break this problem into two subproblems by setting 
(x + -45) equal to 43.531597719 and -43.531597719.

Subproblem 1

x + -45 = 43.531597719 Simplifying x + -45 = 43.531597719 Reorder the terms: -45 + x = 43.531597719 Solving -45 + x = 43.531597719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 43.531597719 + 45 Combine like terms: -45 + 45 = 0 0 + x = 43.531597719 + 45 x = 43.531597719 + 45 Combine like terms: 43.531597719 + 45 = 88.531597719 x = 88.531597719 Simplifying x = 88.531597719

Subproblem 2

x + -45 = -43.531597719 Simplifying x + -45 = -43.531597719 Reorder the terms: -45 + x = -43.531597719 Solving -45 + x = -43.531597719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -43.531597719 + 45 Combine like terms: -45 + 45 = 0 0 + x = -43.531597719 + 45 x = -43.531597719 + 45 Combine like terms: -43.531597719 + 45 = 1.468402281 x = 1.468402281 Simplifying x = 1.468402281

Solution

The solution to the problem is based on the solutions from the subproblems. x = {88.531597719, 1.468402281}

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