2x^2+2x-16.5=0

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Solution for 2x^2+2x-16.5=0 equation:


Simplifying
2x2 + 2x + -16.5 = 0

Reorder the terms:
-16.5 + 2x + 2x2 = 0

Solving
-16.5 + 2x + 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'.
-8.25 + x + x2 = 0

Move the constant term to the right:

Add '8.25' to each side of the equation.
-8.25 + x + 8.25 + x2 = 0 + 8.25

Reorder the terms:
-8.25 + 8.25 + x + x2 = 0 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x + x2 = 0 + 8.25
x + x2 = 0 + 8.25

Combine like terms: 0 + 8.25 = 8.25
x + x2 = 8.25

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 8.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 8.25 + 0.25

Combine like terms: 8.25 + 0.25 = 8.5
1.25 + x2 = 8.5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.915475947 and -2.915475947.

Subproblem 1

x + 0.5 = 2.915475947 Simplifying x + 0.5 = 2.915475947 Reorder the terms: 0.5 + x = 2.915475947 Solving 0.5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.915475947 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.915475947 + -0.5 x = 2.915475947 + -0.5 Combine like terms: 2.915475947 + -0.5 = 2.415475947 x = 2.415475947 Simplifying x = 2.415475947

Subproblem 2

x + 0.5 = -2.915475947 Simplifying x + 0.5 = -2.915475947 Reorder the terms: 0.5 + x = -2.915475947 Solving 0.5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.915475947 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.915475947 + -0.5 x = -2.915475947 + -0.5 Combine like terms: -2.915475947 + -0.5 = -3.415475947 x = -3.415475947 Simplifying x = -3.415475947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.415475947, -3.415475947}

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