-.5(x+3)(x-4)=0

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Solution for -.5(x+3)(x-4)=0 equation:


Simplifying
-0.5(x + 3)(x + -4) = 0
Reorder the terms:
-0.5(3 + x)(x + -4) = 0
Reorder the terms:
-0.5(3 + x)(-4 + x) = 0
Multiply (3 + x) * (-4 + x)
-0.5(3(-4 + x) + x(-4 + x)) = 0
-0.5((-4 * 3 + x * 3) + x(-4 + x)) = 0
-0.5((-12 + 3x) + x(-4 + x)) = 0
-0.5(-12 + 3x + (-4 * x + x * x)) = 0
-0.5(-12 + 3x + (-4x + x2)) = 0
Combine like terms: 3x + -4x = -1x
-0.5(-12 + -1x + x2) = 0
(-12 * -0.5 + -1x * -0.5 + x2 * -0.5) = 0
(6 + 0.5x + -0.5x2) = 0
Solving
6 + 0.5x + -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'.
-12 + -1x + x2 = 0
Move the constant term to the right:
Add '12' to each side of the equation.
-12 + -1x + 12 + x2 = 0 + 12
Reorder the terms:
-12 + 12 + -1x + x2 = 0 + 12
Combine like terms: -12 + 12 = 0
0 + -1x + x2 = 0 + 12
-1x + x2 = 0 + 12
Combine like terms: 0 + 12 = 12
-1x + x2 = 12
The x term is -1x. Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.
Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 12 + 0.25
Reorder the terms:
0.25 + -1x + x2 = 12 + 0.25
Combine like terms: 12 + 0.25 = 12.25
0.25 + -1x + x2 = 12.25
Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 12.25
Calculate the square root of the right side: 3.5
Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.5 and -3.5.

Subproblem 1

x + -0.5 = 3.5 Simplifying x + -0.5 = 3.5 Reorder the terms: -0.5 + x = 3.5 Solving -0.5 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.5 + 0.5 x = 3.5 + 0.5 Combine like terms: 3.5 + 0.5 = 4 x = 4 Simplifying x = 4

Subproblem 2

x + -0.5 = -3.5 Simplifying x + -0.5 = -3.5 Reorder the terms: -0.5 + x = -3.5 Solving -0.5 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.5 + 0.5 x = -3.5 + 0.5 Combine like terms: -3.5 + 0.5 = -3 x = -3 Simplifying x = -3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4, -3}

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