\( (8-2 x)(11-2 x)=18 \) The dimensions of the rug should be (Use a comma to separate answers as needed.)

To solve the equation \( (8-2x)(11-2x)=18 \), we first expand the left side: \[ 88 - 22x - 16x + 4x^2 = 18 \] \[ 4x^2 - 38x + 88 - 18 = 0 \] \[ 4x^2 - 38x + 70 = 0 \] Next, we simplify the quadratic equation by dividing everything by 2: \[ 2x^2 - 19x + 35 = 0 \] Now, we can factor or use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \): For \( a = 2, b = -19, c = 35 \): Discriminant: \( b^2 - 4ac = (-19)^2 - 4(2)(35) = 361 - 280 = 81 \) Square root of 81 is 9. Calculating the two potential values for \( x \): \[ x = \frac{19 \pm 9}{4} \] 1. \( x = \frac{28}{4} = 7 \) 2. \( x = \frac{10}{4} = 2.5 \) Thus, the dimensions of the rug are \( 7, 2.5 \).