0.5x^2-(-x+4)=0

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Solution for 0.5x^2-(-x+4)=0 equation:


Simplifying
0.5x2 + -1(-1x + 4) = 0

Reorder the terms:
0.5x2 + -1(4 + -1x) = 0
0.5x2 + (4 * -1 + -1x * -1) = 0
0.5x2 + (-4 + 1x) = 0

Reorder the terms:
-4 + 1x + 0.5x2 = 0

Solving
-4 + 1x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-8 + 2x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 2x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 2x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2x + x2 = 0 + 8
2x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
2x + x2 = 8

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 = 8 + 1

Reorder the terms:
1 + 2x + x2 = 8 + 1

Combine like terms: 8 + 1 = 9
1 + 2x + x2 = 9

Factor a perfect square on the left side:
(x + 1)(x + 1) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + 1) equal to 3 and -3.

Subproblem 1

x + 1 = 3 Simplifying x + 1 = 3 Reorder the terms: 1 + x = 3 Solving 1 + x = 3 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 = 3 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3 + -1 x = 3 + -1 Combine like terms: 3 + -1 = 2 x = 2 Simplifying x = 2

Subproblem 2

x + 1 = -3 Simplifying x + 1 = -3 Reorder the terms: 1 + x = -3 Solving 1 + x = -3 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 = -3 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3 + -1 x = -3 + -1 Combine like terms: -3 + -1 = -4 x = -4 Simplifying x = -4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2, -4}

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