(x-2)(x+3)+14=0

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Solution for (x-2)(x+3)+14=0 equation:


Simplifying
(x + -2)(x + 3) + 14 = 0

Reorder the terms:
(-2 + x)(x + 3) + 14 = 0

Reorder the terms:
(-2 + x)(3 + x) + 14 = 0

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) + 14 = 0
((3 * -2 + x * -2) + x(3 + x)) + 14 = 0
((-6 + -2x) + x(3 + x)) + 14 = 0
(-6 + -2x + (3 * x + x * x)) + 14 = 0
(-6 + -2x + (3x + x2)) + 14 = 0

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) + 14 = 0

Reorder the terms:
-6 + 14 + 1x + x2 = 0

Combine like terms: -6 + 14 = 8
8 + 1x + x2 = 0

Solving
8 + 1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 1x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 1x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 1x + x2 = 0 + -8
1x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
1x + x2 = -8

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.
x + 0.25 + x2 = -8 + 0.25

Reorder the terms:
0.25 + x + x2 = -8 + 0.25

Combine like terms: -8 + 0.25 = -7.75
0.25 + x + x2 = -7.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -7.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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