Answer:
x2 + 8x – 65 = 0
Explanation:
Complete question
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches. Which equation can be used to solve for x, the increase in side length of the square in inches? x2 + 4x – 81 = 0 x2 + 4x – 65 = 0 x2 + 8x – 65 = 0 x2 + 8x – 81 = 0
Given the initial side length = 4in
Initial area = L²
L is side length of the square
Initial area = 4²
Initial area = 16 square inches
Area of the enlarged square = 81 square inches
To get the constant term of the expression, we will find the difference in the areas
Difference = 85 - 16
Difference = 65 square units
The coefficient of x will be the 2 *initial area of the square
Given the standard form of an expression as
ax^2 + bx + c
a = 1, b = 2*4 = 8, c = -65
Substitute
x^2 + 8x - 65
This gives the required expression