# -.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 1x + -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 2x + -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
SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {4, -3}`