(x+1.16)(x-0.5)=

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Solution for (x+1.16)(x-0.5)= equation:


Simplifying
(x + 1.16)(x + -0.5) = 0

Reorder the terms:
(1.16 + x)(x + -0.5) = 0

Reorder the terms:
(1.16 + x)(-0.5 + x) = 0

Multiply (1.16 + x) * (-0.5 + x)
(1.16(-0.5 + x) + x(-0.5 + x)) = 0
((-0.5 * 1.16 + x * 1.16) + x(-0.5 + x)) = 0
((-0.58 + 1.16x) + x(-0.5 + x)) = 0
(-0.58 + 1.16x + (-0.5 * x + x * x)) = 0
(-0.58 + 1.16x + (-0.5x + x2)) = 0

Combine like terms: 1.16x + -0.5x = 0.66x
(-0.58 + 0.66x + x2) = 0

Solving
-0.58 + 0.66x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.58' to each side of the equation.
-0.58 + 0.66x + 0.58 + x2 = 0 + 0.58

Reorder the terms:
-0.58 + 0.58 + 0.66x + x2 = 0 + 0.58

Combine like terms: -0.58 + 0.58 = 0.00
0.00 + 0.66x + x2 = 0 + 0.58
0.66x + x2 = 0 + 0.58

Combine like terms: 0 + 0.58 = 0.58
0.66x + x2 = 0.58

The x term is 0.66x.  Take half its coefficient (0.33).
Square it (0.1089) and add it to both sides.

Add '0.1089' to each side of the equation.
0.66x + 0.1089 + x2 = 0.58 + 0.1089

Reorder the terms:
0.1089 + 0.66x + x2 = 0.58 + 0.1089

Combine like terms: 0.58 + 0.1089 = 0.6889
0.1089 + 0.66x + x2 = 0.6889

Factor a perfect square on the left side:
(x + 0.33)(x + 0.33) = 0.6889

Calculate the square root of the right side: 0.83

Break this problem into two subproblems by setting 
(x + 0.33) equal to 0.83 and -0.83.


Subproblem 1
x + 0.33 = 0.83

Simplifying
x + 0.33 = 0.83

Reorder the terms:
0.33 + x = 0.83

Solving
0.33 + x = 0.83

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.33' to each side of the equation.
0.33 + -0.33 + x = 0.83 + -0.33

Combine like terms: 0.33 + -0.33 = 0.00
0.00 + x = 0.83 + -0.33
x = 0.83 + -0.33

Combine like terms: 0.83 + -0.33 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 0.33 = -0.83

Simplifying
x + 0.33 = -0.83

Reorder the terms:
0.33 + x = -0.83

Solving
0.33 + x = -0.83

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.33' to each side of the equation.
0.33 + -0.33 + x = -0.83 + -0.33

Combine like terms: 0.33 + -0.33 = 0.00
0.00 + x = -0.83 + -0.33
x = -0.83 + -0.33

Combine like terms: -0.83 + -0.33 = -1.16
x = -1.16

Simplifying
x = -1.16


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -1.16}

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