Sure, let's solve the two given quadratic equations step-by-step.
### 1. Solve [tex]\( y^2 = 100 \)[/tex]
To find the value of [tex]\( y \)[/tex], we need to take the square root of both sides of the equation.
[tex]\[ y^2 = 100 \][/tex]
Taking the square root of both sides gives:
[tex]\[ y = \pm \sqrt{100} \][/tex]
Since [tex]\( \sqrt{100} = 10 \)[/tex], we have two solutions:
[tex]\[ y = 10 \quad \text{and} \quad y = -10 \][/tex]
### 2. Solve [tex]\( 6.2 x^2 - 8 = 80 \)[/tex]
First, we need to simplify the equation:
[tex]\[ 6.2 x^2 - 8 = 80 \][/tex]
Add 8 to both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ 6.2 x^2 = 88 \][/tex]
Next, divide both sides of the equation by 6.2 to solve for [tex]\( x^2 \)[/tex]:
[tex]\[ x^2 = \frac{88}{6.2} \][/tex]
Performing the division:
[tex]\[ x^2 \approx 14.193548 \][/tex]
Taking the square root of both sides gives:
[tex]\[ x \approx \pm \sqrt{14.193548} \][/tex]
Therefore, the solutions for [tex]\( x \)[/tex] are:
[tex]\[ x \approx 3.767 \quad \text{and} \quad x \approx -3.767 \][/tex]
In summary, the solutions for the given quadratic equations are:
For [tex]\( y^2 = 100 \)[/tex]:
[tex]\[ y = 10 \quad \text{and} \quad y = -10 \][/tex]
For [tex]\( 6.2 x^2 - 8 = 80 \)[/tex]:
[tex]\[ x \approx 3.767 \quad \text{and} \quad x \approx -3.767 \][/tex]
