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Answer:
see explanation
Step-by-step explanation:
x² - 8x - 9 = 0 ← in standard form
(x - 9)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 9 = 0 ⇒ x = 9
x + 1 = 0 ⇒ x = - 1
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100x² - 20x = 0 ( divide through by 20 )
5x² - x = 0 ( factor out x from each term )
x(5x - 1) = 0
x = 0
5x - 1 = 0 ⇒ 5x = 1 ⇒ x = [tex]\frac{1}{5}[/tex]
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2x² - 7x - 15 = 0 ← in standard form
(2x + 3)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]
x - 5 = 0 ⇒ x = 5
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x² + 9x + 13 = - 5x - 20 (add 5x + 20 to both sides )
x² + 14x + 33 = 0 ← in standard form
(x + 11)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 11 = 0 ⇒ x = - 11
x + 3 = 0 ⇒ x = - 3
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3x² - 12x + 5 = 9 - 4x² ( subtract 9 - 4x² from both sides )
7x² - 12x - 4 = 0 ← in standard form
(7x + 2)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
7x + 2 = 0 ⇒ 7x = - 2 ⇒ x = - [tex]\frac{2}{7}[/tex]
x - 2 = 0 ⇒ x = 2
Solution set of the given quadratic equations are
1. x = 9 or x = -1
2. x=0 or x = 1 / 5
3. x= 5 or x = -3/2
4. x= -11 or x= -3
5. x= 2 or x= -2/7
What is quadratic equation?
" Quadratic equation is an algebraic expression in which highest degree of the given variable is 2."
Formula used
x² +ax + b = (x + c)(x + d)
Where 'a' is the sum 'c' and 'd'
and 'b' is the product of 'c' and 'd'
According to the question,
Factorize all the given quadratic equations we get,
1. x² - 8x - 9 =0
Split middle term of quadratic equation using formula we get,
x² - 9x + x -9 =0
⇒ x(x-9) +1(x - 9) =0
⇒(x -9)(x +1) =0
⇒ x- 9 =0 or x + 1 =0
⇒ x= 9 or x =-1
2. 100x² -20x =0
⇒20x( 5x -1) =0
⇒ 20 ≠ 0, x=0 or 5x - 1=0
⇒ x =0 or x = 1/5
3. 2x² -7x -15 =0
Split middle term of quadratic equation using formula we get,
2x² -10x + 3x -15 =0
⇒ 2x(x-5) +3(x-5)=0
⇒(2x+3)(x-5)=0
⇒2x+3 =0 or x-5 =0
⇒ x= -3/2 or x=5
4. x² +9x +13 = -5x -20
⇒x² +9x + 5x+13 + 20 = 0
⇒x² +14x +33 =0
Split middle term of quadratic equation using formula we get,
x² +11x +3x+33 =0
⇒x(x+11) +3(x+11) =0
⇒(x+3)(x+11) =0
⇒ x= -3 or x=-11
5. 3x² -12x +5 = 9- 4x²
⇒3x²+4x² -12x +5 -9 =0
⇒7x² -12x -4=0
Split middle term of quadratic equation using formula we get,
⇒7x² -14x +2x -4 =0
⇒7x(x-2) +2(x-2)=0
⇒(7x+2)(x-2)=0
⇒7x+2 =0 or x-2 =0
⇒x = -2/7 or x=2
Hence, the solution set of the given quadratic equations are
1. x = 9 or x = -1
2. x=0 or x = 1 / 5
3. x= 5 or x = -3/2
4. x= -11 or x= -3
5. x= 2 or x= -2/7
Learn more about quadratic equation here
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