Answer :
We start with the equation
[tex]$$29z^2 + 144 = 218.$$[/tex]
Step 1. Subtract 144 from both sides.
Subtracting 144 from both sides gives:
[tex]$$29z^2 = 218 - 144 = 74.$$[/tex]
Step 2. Divide both sides by 29.
Dividing by 29 isolates [tex]$z^2$[/tex]:
[tex]$$z^2 = \frac{74}{29} \approx 2.5517241379310347.$$[/tex]
Step 3. Take the square root of both sides.
Since taking the square root yields two solutions (one positive and one negative), we have:
[tex]$$z = \sqrt{\frac{74}{29}} \quad \text{or} \quad z = -\sqrt{\frac{74}{29}}.$$[/tex]
Numerically, the solutions are approximately:
[tex]$$z \approx 1.5974116995724785 \quad \text{or} \quad z \approx -1.5974116995724785.$$[/tex]
Thus, the solutions to the equation are
[tex]$$z \approx 1.5974 \quad \text{and} \quad z \approx -1.5974.$$[/tex]
[tex]$$29z^2 + 144 = 218.$$[/tex]
Step 1. Subtract 144 from both sides.
Subtracting 144 from both sides gives:
[tex]$$29z^2 = 218 - 144 = 74.$$[/tex]
Step 2. Divide both sides by 29.
Dividing by 29 isolates [tex]$z^2$[/tex]:
[tex]$$z^2 = \frac{74}{29} \approx 2.5517241379310347.$$[/tex]
Step 3. Take the square root of both sides.
Since taking the square root yields two solutions (one positive and one negative), we have:
[tex]$$z = \sqrt{\frac{74}{29}} \quad \text{or} \quad z = -\sqrt{\frac{74}{29}}.$$[/tex]
Numerically, the solutions are approximately:
[tex]$$z \approx 1.5974116995724785 \quad \text{or} \quad z \approx -1.5974116995724785.$$[/tex]
Thus, the solutions to the equation are
[tex]$$z \approx 1.5974 \quad \text{and} \quad z \approx -1.5974.$$[/tex]
