<h2>Solving Quadratic Equations by Completing the Square</h2><h3>
Answer:</h3>
and ![a = -3](https://tex.z-dn.net/?f=a%20%3D%20-3)
<h3>
Step-by-step explanation:</h3>
Solving by Completing the Square:
![a^2 +2a -3 = 0 \\ a^2 +2a -3 +3 = 0 +3 \\ a^2 +2a = 3 \\ a^2 +2a +1 = 3 +1 \\ (a +1)^2 = 4 \\ \sqrt{(a +1)^2} = \pm \sqrt{4} \\ a +1 = \pm 2](https://tex.z-dn.net/?f=a%5E2%20%2B2a%20-3%20%3D%200%20%5C%5C%20a%5E2%20%2B2a%20-3%20%2B3%20%3D%200%20%2B3%20%5C%5C%20a%5E2%20%2B2a%20%3D%203%20%5C%5C%20a%5E2%20%2B2a%20%2B1%20%3D%203%20%2B1%20%5C%5C%20%28a%20%2B1%29%5E2%20%3D%204%20%5C%5C%20%5Csqrt%7B%28a%20%2B1%29%5E2%7D%20%3D%20%5Cpm%20%5Csqrt%7B4%7D%20%5C%5C%20a%20%2B1%20%3D%20%5Cpm%202)
Solving for
from the positive root:
![a +1 = 2 \\ a +1 -1 = 2 -1 \\ a = 1](https://tex.z-dn.net/?f=a%20%2B1%20%3D%202%20%5C%5C%20a%20%2B1%20-1%20%3D%202%20-1%20%5C%5C%20a%20%3D%201)
Solving for
from the negative root:
![a +1 = -2 \\ a +1 -1 = -2 -1 \\ a = -3](https://tex.z-dn.net/?f=a%20%2B1%20%3D%20-2%20%5C%5C%20a%20%2B1%20-1%20%3D%20-2%20-1%20%5C%5C%20a%20%3D%20-3)
The solutions are
and ![a = -3](https://tex.z-dn.net/?f=a%20%3D%20-3)
Answer:
B. 5.4
Step-by-step explanation:
3/5 = 6/10
6/10 = 0.6
9 x 0.6 = 5.4
Answer:
a = A/πb
Step-by-step explanation:
To solve this subject of the formulae given that A = πab.
<u>solution</u>
A = πab
the next step is to look for a unique way to get rid of the variables disturbing "a" from standing alone. this variables are π and b, we need to detach dem from a
A = πab
divide both sides by πb
A/πb = πab/πb
A/πb = a
a = A/πb
therefore the value of a in the fomular A = πab is evaluated to be a = A/πb
Answer: 4x² + 5x + 3
<u>Step-by-step explanation:</u>
![\dfrac{4x^3+5x^2+3x}{x}\\\\\\=\dfrac{x(4x^2+5x+3)}{x}\qquad \text{factored out the common term from the numerator}\\\\\\=4x^2+5x+3\qquad \text{canceled out x from numerator and denominator}](https://tex.z-dn.net/?f=%5Cdfrac%7B4x%5E3%2B5x%5E2%2B3x%7D%7Bx%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7Bx%284x%5E2%2B5x%2B3%29%7D%7Bx%7D%5Cqquad%20%5Ctext%7Bfactored%20out%20the%20common%20term%20from%20the%20numerator%7D%5C%5C%5C%5C%5C%5C%3D4x%5E2%2B5x%2B3%5Cqquad%20%5Ctext%7Bcanceled%20out%20x%20from%20numerator%20and%20denominator%7D)
Answer:
36m²
Step-by-step explanation:
<em>Area </em><em>of </em><em>triangle </em><em>=</em><em> </em><em>1</em><em>/</em><em>2</em><em>x</em><em> </em><em>base </em><em>x </em><em>height </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>Area of triangle</em><em> </em><em>=</em><em>1</em><em>/</em><em>2</em><em>x</em><em> </em><em>1</em><em>2</em><em> </em><em>x6</em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em>
<em>Area of triangle</em><em> </em><em> </em><em> </em><em>=</em><em>6</em><em>x</em><em>6</em><em> </em>
<em>Area of </em><em>triangle</em><em> </em><em> </em><em>=</em><em>3</em><em>6</em><em>m</em><em>²</em>