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3 years ago

Simplify -11 sqrt 112.

Mathematics

1 answer:

9966 [12]3 years ago

4 0

The answer should be -44√7 because:
1. √112 is √16 times √7
2. √16 is 4
3. -11(4√7)=-44√7

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Solve - 4x2 - 4x - 9 = 0, stating your solutions in the form a = bi. Someone please answer!!

PIT_PIT [208]

Answer:

$x=-0.5 \pm -i\sqrt{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Algebra II

Imaginary Roots: √-1 = i
Standard Form: a + bi

Step-by-step explanation:

Step 1: Define

-4x² - 4x - 9 = 0

a = -4

b = -4

c = -9

Step 2: Find roots

Substitute: $x=\frac{4\pm\sqrt{(-4)^2-4(-4)(-9)} }{2(-4)}$
Exponents: $x=\frac{4\pm\sqrt{16-4(-4)(-9)} }{2(-4)}$
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Subtract: $x=\frac{4\pm\sqrt{-128} }{-8}$
Factor: $x=\frac{4\pm \sqrt{-1} \cdot \sqrt{128} }{-8}$
Simplify: $x=\frac{4\pm 8i\sqrt{2} }{-8}$
Factor: $x=\frac{4(1\pm 2i\sqrt{2}) }{-8}$
Divide: $x=\frac{1\pm 2i\sqrt{2}}{-2}$
Expand: $x=\frac{-1}{2} \pm \frac{-2i\sqrt{2} }{2}$
Simplify: $x=\frac{-1}{2} \pm -i\sqrt{2}$
Evaluate: $x=-0.5 \pm -i\sqrt{2}$

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