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1 month ago

Solve the following quadratic equations by extracting square roots.Answer the questions that follow.

Mathematics

2 answers:

Leona [12.6K]1 month ago

8 0

Answer:

$1.+4,-4\\2. +9,-9\\3. +10,-10\\4. +12, -12\\5. +5, -5$

Step-by-step explanation:

To find the solution for quadratic equations, focus on extracting the square root of the constant term:

$x^{2} =16\\x=\sqrt{16}\\ x= +4, -4$

$t^{2} =16\\t=\sqrt{81}\\ x= +9, -9$

$r^{2} =100\\r=\sqrt{100}\\ x= +10, -10$

$x^{2} -144=0\\x=\sqrt{144}\\ x= +12, -12$

$2s^{2}=50\\s^{2}=\frac{50}{2} \\s=\sqrt{25}\\ s= +5, -5$

Keep in mind, every square root yields both positive and negative values as answers.

babunello [11.8K]1 month ago

4 0

Answer:

1. x=±4

2. t=±9

3. r=±10

4. x=±12

5. s=±5

Step-by-step explanation:

1. x^2 = 16

By extracting the square root on both sides

$\sqrt{x^2}=\sqrt{16}\\\sqrt{x^2}=\sqrt{(4)^2}\\$

x=±4

2. t^2=81

Again, take the square root of each side

$\sqrt{t^2}=\sqrt{81}\\\sqrt{t^2}=\sqrt{(9)^2}$

t=±9

3. r^2-100=0

$r^{2}-100=0\\r^2 =100\\Taking\ Square\ root\ on\ both\ sides\\\sqrt{r^2}=\sqrt{100}\\\sqrt{r^2}=\sqrt{(10)^2}$

r=±10

4. x²-144=0

We rewrite as x²=144

Applying square roots

$\sqrt{x^2}=\sqrt{144}\\\sqrt{x^2}=\sqrt{(12)^2}$

x=±12

5. 2s²=50

$\frac{2s^2}{2} =\frac{50}{2}\\s^2=25\\Taking\ Square\ root\ on\ both\ sides\\\sqrt{s^2}=\sqrt{25}\\\sqrt{s^2}=\sqrt{(5)^2}$

s=±5 ..

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