2x^2-23x+24=0

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Solution for 2x^2-23x+24=0 equation:


Simplifying
2x2 + -23x + 24 = 0

Reorder the terms:
24 + -23x + 2x2 = 0

Solving
24 + -23x + 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'.
12 + -11.5x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -11.5x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -11.5x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -11.5x + x2 = 0 + -12
-11.5x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-11.5x + x2 = -12

The x term is -11.5x.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x2 = -12 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = -12 + 33.0625

Combine like terms: -12 + 33.0625 = 21.0625
33.0625 + -11.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + -5.75) equal to 4.589389938 and -4.589389938.

Subproblem 1

x + -5.75 = 4.589389938 Simplifying x + -5.75 = 4.589389938 Reorder the terms: -5.75 + x = 4.589389938 Solving -5.75 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 4.589389938 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 4.589389938 + 5.75 x = 4.589389938 + 5.75 Combine like terms: 4.589389938 + 5.75 = 10.339389938 x = 10.339389938 Simplifying x = 10.339389938

Subproblem 2

x + -5.75 = -4.589389938 Simplifying x + -5.75 = -4.589389938 Reorder the terms: -5.75 + x = -4.589389938 Solving -5.75 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -4.589389938 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -4.589389938 + 5.75 x = -4.589389938 + 5.75 Combine like terms: -4.589389938 + 5.75 = 1.160610062 x = 1.160610062 Simplifying x = 1.160610062

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.339389938, 1.160610062}

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