2x^2+11.4x-696.51=0

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Solution for 2x^2+11.4x-696.51=0 equation:


Simplifying
2x2 + 11.4x + -696.51 = 0

Reorder the terms:
-696.51 + 11.4x + 2x2 = 0

Solving
-696.51 + 11.4x + 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'.
-348.255 + 5.7x + x2 = 0

Move the constant term to the right:

Add '348.255' to each side of the equation.
-348.255 + 5.7x + 348.255 + x2 = 0 + 348.255

Reorder the terms:
-348.255 + 348.255 + 5.7x + x2 = 0 + 348.255

Combine like terms: -348.255 + 348.255 = 0.000
0.000 + 5.7x + x2 = 0 + 348.255
5.7x + x2 = 0 + 348.255

Combine like terms: 0 + 348.255 = 348.255
5.7x + x2 = 348.255

The x term is 5.7x.  Take half its coefficient (2.85).
Square it (8.1225) and add it to both sides.

Add '8.1225' to each side of the equation.
5.7x + 8.1225 + x2 = 348.255 + 8.1225

Reorder the terms:
8.1225 + 5.7x + x2 = 348.255 + 8.1225

Combine like terms: 348.255 + 8.1225 = 356.3775
8.1225 + 5.7x + x2 = 356.3775

Factor a perfect square on the left side:
(x + 2.85)(x + 2.85) = 356.3775

Calculate the square root of the right side: 18.877963344

Break this problem into two subproblems by setting 
(x + 2.85) equal to 18.877963344 and -18.877963344.

Subproblem 1

x + 2.85 = 18.877963344 Simplifying x + 2.85 = 18.877963344 Reorder the terms: 2.85 + x = 18.877963344 Solving 2.85 + x = 18.877963344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.85' to each side of the equation. 2.85 + -2.85 + x = 18.877963344 + -2.85 Combine like terms: 2.85 + -2.85 = 0.00 0.00 + x = 18.877963344 + -2.85 x = 18.877963344 + -2.85 Combine like terms: 18.877963344 + -2.85 = 16.027963344 x = 16.027963344 Simplifying x = 16.027963344

Subproblem 2

x + 2.85 = -18.877963344 Simplifying x + 2.85 = -18.877963344 Reorder the terms: 2.85 + x = -18.877963344 Solving 2.85 + x = -18.877963344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.85' to each side of the equation. 2.85 + -2.85 + x = -18.877963344 + -2.85 Combine like terms: 2.85 + -2.85 = 0.00 0.00 + x = -18.877963344 + -2.85 x = -18.877963344 + -2.85 Combine like terms: -18.877963344 + -2.85 = -21.727963344 x = -21.727963344 Simplifying x = -21.727963344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.027963344, -21.727963344}

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