Question

Use the square root property to find all solutions to (7p+2)²=75

Answer 1

To solve (7p+2)²=75, take the square root of both sides resulting in two potential solutions for p, which are (-2 + √75) / 7 and (-2 - √75) / 7.

Step-by-step explanation:

To solve the equation (7p+2)²=75 using the square root property, we first take the square root of both sides of the equation. This yields two possible solutions because the square root of a number can be either positive or negative. The steps are as follows:

1. Take the square root of both sides of the equation, remembering to include both the positive and negative roots: √(7p+2)² = ±√75.
2. Simplify the square root of the left side to get 7p+2 and simplify the right side to ±√75.
3. To find the two solutions for p, subtract 2 from both sides of each equation and then divide by 7: p = (±√75 - 2) / 7.

Therefore, the solutions for p are (-2 + √75) / 7 and (-2 - √75) / 7.