2x^2+9.42x-50.8=0

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Solution for 2x^2+9.42x-50.8=0 equation:


Simplifying
2x2 + 9.42x + -50.8 = 0

Reorder the terms:
-50.8 + 9.42x + 2x2 = 0

Solving
-50.8 + 9.42x + 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'.
-25.4 + 4.71x + x2 = 0

Move the constant term to the right:

Add '25.4' to each side of the equation.
-25.4 + 4.71x + 25.4 + x2 = 0 + 25.4

Reorder the terms:
-25.4 + 25.4 + 4.71x + x2 = 0 + 25.4

Combine like terms: -25.4 + 25.4 = 0.0
0.0 + 4.71x + x2 = 0 + 25.4
4.71x + x2 = 0 + 25.4

Combine like terms: 0 + 25.4 = 25.4
4.71x + x2 = 25.4

The x term is 4.71x.  Take half its coefficient (2.355).
Square it (5.546025) and add it to both sides.

Add '5.546025' to each side of the equation.
4.71x + 5.546025 + x2 = 25.4 + 5.546025

Reorder the terms:
5.546025 + 4.71x + x2 = 25.4 + 5.546025

Combine like terms: 25.4 + 5.546025 = 30.946025
5.546025 + 4.71x + x2 = 30.946025

Factor a perfect square on the left side:
(x + 2.355)(x + 2.355) = 30.946025

Calculate the square root of the right side: 5.562915153

Break this problem into two subproblems by setting 
(x + 2.355) equal to 5.562915153 and -5.562915153.

Subproblem 1

x + 2.355 = 5.562915153 Simplifying x + 2.355 = 5.562915153 Reorder the terms: 2.355 + x = 5.562915153 Solving 2.355 + x = 5.562915153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.355' to each side of the equation. 2.355 + -2.355 + x = 5.562915153 + -2.355 Combine like terms: 2.355 + -2.355 = 0.000 0.000 + x = 5.562915153 + -2.355 x = 5.562915153 + -2.355 Combine like terms: 5.562915153 + -2.355 = 3.207915153 x = 3.207915153 Simplifying x = 3.207915153

Subproblem 2

x + 2.355 = -5.562915153 Simplifying x + 2.355 = -5.562915153 Reorder the terms: 2.355 + x = -5.562915153 Solving 2.355 + x = -5.562915153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.355' to each side of the equation. 2.355 + -2.355 + x = -5.562915153 + -2.355 Combine like terms: 2.355 + -2.355 = 0.000 0.000 + x = -5.562915153 + -2.355 x = -5.562915153 + -2.355 Combine like terms: -5.562915153 + -2.355 = -7.917915153 x = -7.917915153 Simplifying x = -7.917915153

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.207915153, -7.917915153}

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