Questions: Use the Square Root Property to solve the quadratic equation 3z^2 + 11 = 14 use a comma to separate solutions z=

Transcript text: Use the Square Root Property to solve the quadratic equation $3 z^{2}+11=14$ use a comma to separate solutions \[ z= \]

Solution

Solution Steps

To solve the quadratic equation $3z^2 + 11 = 14$ using the Square Root Property, follow these steps:

Isolate the quadratic term by subtracting 11 from both sides.
Divide both sides by the coefficient of $z^2$.
Take the square root of both sides, remembering to include both the positive and negative roots.

Step 1: Isolate the Quadratic Term

Starting with the equation $3z^2 + 11 = 14$, we first isolate the quadratic term by subtracting 11 from both sides: \[ 3z^2 = 14 - 11 \] This simplifies to: \[ 3z^2 = 3 \]

Step 2: Divide by the Coefficient

Next, we divide both sides by 3 to solve for $z^2$: \[ z^2 = \frac{3}{3} \] This simplifies to: \[ z^2 = 1 \]

Step 3: Take the Square Root

Now, we take the square root of both sides, remembering to consider both the positive and negative roots: \[ z = \sqrt{1} \quad \text{or} \quad z = -\sqrt{1} \] This gives us the solutions: \[ z = 1 \quad \text{and} \quad z = -1 \]