-2x^2-4x+16=1

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Solution for -2x^2-4x+16=1 equation:


Simplifying
-2x2 + -4x + 16 = 1

Reorder the terms:
16 + -4x + -2x2 = 1

Solving
16 + -4x + -2x2 = 1

Solving for variable 'x'.

Reorder the terms:
16 + -1 + -4x + -2x2 = 1 + -1

Combine like terms: 16 + -1 = 15
15 + -4x + -2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
15 + -4x + -2x2 = 0

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

Divide each side by '-2'.
-7.5 + 2x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 2x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 2x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 2x + x2 = 0 + 7.5
2x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
2x + x2 = 7.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 7.5 + 1

Reorder the terms:
1 + 2x + x2 = 7.5 + 1

Combine like terms: 7.5 + 1 = 8.5
1 + 2x + x2 = 8.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + 1) equal to 2.915475947 and -2.915475947.

Subproblem 1

x + 1 = 2.915475947 Simplifying x + 1 = 2.915475947 Reorder the terms: 1 + x = 2.915475947 Solving 1 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.915475947 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.915475947 + -1 x = 2.915475947 + -1 Combine like terms: 2.915475947 + -1 = 1.915475947 x = 1.915475947 Simplifying x = 1.915475947

Subproblem 2

x + 1 = -2.915475947 Simplifying x + 1 = -2.915475947 Reorder the terms: 1 + x = -2.915475947 Solving 1 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.915475947 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.915475947 + -1 x = -2.915475947 + -1 Combine like terms: -2.915475947 + -1 = -3.915475947 x = -3.915475947 Simplifying x = -3.915475947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.915475947, -3.915475947}

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