0.5x^2+4x-10=0

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Solution for 0.5x^2+4x-10=0 equation:


Simplifying
0.5x2 + 4x + -10 = 0

Reorder the terms:
-10 + 4x + 0.5x2 = 0

Solving
-10 + 4x + 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'.
-20 + 8x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 8x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 8x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 8x + x2 = 0 + 20
8x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
8x + x2 = 20

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 = 20 + 16

Reorder the terms:
16 + 8x + x2 = 20 + 16

Combine like terms: 20 + 16 = 36
16 + 8x + x2 = 36

Factor a perfect square on the left side:
(x + 4)(x + 4) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + 4) equal to 6 and -6.

Subproblem 1

x + 4 = 6 Simplifying x + 4 = 6 Reorder the terms: 4 + x = 6 Solving 4 + x = 6 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 = 6 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6 + -4 x = 6 + -4 Combine like terms: 6 + -4 = 2 x = 2 Simplifying x = 2

Subproblem 2

x + 4 = -6 Simplifying x + 4 = -6 Reorder the terms: 4 + x = -6 Solving 4 + x = -6 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 = -6 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6 + -4 x = -6 + -4 Combine like terms: -6 + -4 = -10 x = -10 Simplifying x = -10

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2, -10}

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