-2x^2+16=-7x

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Solution for -2x^2+16=-7x equation:


Simplifying
-2x2 + 16 = -7x

Reorder the terms:
16 + -2x2 = -7x

Solving
16 + -2x2 = -7x

Solving for variable 'x'.

Reorder the terms:
16 + 7x + -2x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
16 + 7x + -2x2 = 0

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

Divide each side by '-2'.
-8 + -3.5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -3.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3.5x + x2 = 0 + 8
-3.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-3.5x + x2 = 8

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 8 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 8 + 3.0625

Combine like terms: 8 + 3.0625 = 11.0625
3.0625 + -3.5x + x2 = 11.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(x + -1.75) equal to 3.326033674 and -3.326033674.

Subproblem 1

x + -1.75 = 3.326033674 Simplifying x + -1.75 = 3.326033674 Reorder the terms: -1.75 + x = 3.326033674 Solving -1.75 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.326033674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.326033674 + 1.75 x = 3.326033674 + 1.75 Combine like terms: 3.326033674 + 1.75 = 5.076033674 x = 5.076033674 Simplifying x = 5.076033674

Subproblem 2

x + -1.75 = -3.326033674 Simplifying x + -1.75 = -3.326033674 Reorder the terms: -1.75 + x = -3.326033674 Solving -1.75 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.326033674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.326033674 + 1.75 x = -3.326033674 + 1.75 Combine like terms: -3.326033674 + 1.75 = -1.576033674 x = -1.576033674 Simplifying x = -1.576033674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.076033674, -1.576033674}

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