2x^2-5x-22=0

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Solution for 2x^2-5x-22=0 equation:


Simplifying
2x2 + -5x + -22 = 0

Reorder the terms:
-22 + -5x + 2x2 = 0

Solving
-22 + -5x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-11 + -2.5x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -2.5x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -2.5x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2.5x + x2 = 0 + 11
-2.5x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2.5x + x2 = 11

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 11 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 11 + 1.5625

Combine like terms: 11 + 1.5625 = 12.5625
1.5625 + -2.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + -1.25) equal to 3.54436172 and -3.54436172.

Subproblem 1

x + -1.25 = 3.54436172 Simplifying x + -1.25 = 3.54436172 Reorder the terms: -1.25 + x = 3.54436172 Solving -1.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.54436172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.54436172 + 1.25 x = 3.54436172 + 1.25 Combine like terms: 3.54436172 + 1.25 = 4.79436172 x = 4.79436172 Simplifying x = 4.79436172

Subproblem 2

x + -1.25 = -3.54436172 Simplifying x + -1.25 = -3.54436172 Reorder the terms: -1.25 + x = -3.54436172 Solving -1.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.54436172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.54436172 + 1.25 x = -3.54436172 + 1.25 Combine like terms: -3.54436172 + 1.25 = -2.29436172 x = -2.29436172 Simplifying x = -2.29436172

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.79436172, -2.29436172}

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