Question

John's patio is 5 feet by 10 feet. He will be increasing the width and the length each by x feet. He wants the new area of his patio to be at least 126 square feet. Determine all the possible values for x.

Answer 1

Current area is 5ft * 10ft = 50ft^2.

Increasing by x, you have:
$(5 + x)*(10 + x) \geq 126 \\\\ 50 + 5x + 10x + x^2 \geq 126 \\\\ x^2 + 15x - 76 \geq 0 \\\\ x \geq 4, x \geq -19$

Since length must be positive, $x \geq 4$