4x-0.5x^2=-4

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Solution for 4x-0.5x^2=-4 equation:


Simplifying
4x + -0.5x2 = -4

Solving
4x + -0.5x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + 4x + -0.5x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 4x + -0.5x2 = 0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-8 + -8x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 8 + 16

Reorder the terms:
16 + -8x + x2 = 8 + 16

Combine like terms: 8 + 16 = 24
16 + -8x + x2 = 24

Factor a perfect square on the left side:
(x + -4)(x + -4) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -4) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + -4 = 4.898979486 Simplifying x + -4 = 4.898979486 Reorder the terms: -4 + x = 4.898979486 Solving -4 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.898979486 + 4 x = 4.898979486 + 4 Combine like terms: 4.898979486 + 4 = 8.898979486 x = 8.898979486 Simplifying x = 8.898979486

Subproblem 2

x + -4 = -4.898979486 Simplifying x + -4 = -4.898979486 Reorder the terms: -4 + x = -4.898979486 Solving -4 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.898979486 + 4 x = -4.898979486 + 4 Combine like terms: -4.898979486 + 4 = -0.898979486 x = -0.898979486 Simplifying x = -0.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.898979486, -0.898979486}

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