Rizul N. answered • 12/24/12

UNC-CH Grad For Math and Science Tutor

**4x(6x+6)=38**

**Step 1: Distribute** 24x^{2} + 24x = 38

**Step 2: Get rid of coefficient in front of x ^{2}, so factoring is easier.**

x^{2} + x = ^{38}/_{24}

**Step 3: Reduce the fraction on the right side.**

x^{2} + x = ^{19}/_{12}

**Step 4: ****Complete the square on the left side.**

x^{2} + x + ^{1}/_{4} = ^{19}/_{12} + ^{1}/_{4}

**Step 5: factor the equation on the left and reduce the numerical expression on the right.**

(x + ^{1}/_{2})^{2} = ^{22}/_{12}

**Step 6: In order to solve for x, take the square root of the number on the right side. **

(x + ^{1}/_{2}) = **(plus or minus)** sqrt (^{22}/_{12})

**Step 7:** **x = ^{1}/_{6} (-3 - sqrt(66))**

** x = ^{1}/_{6} (sqrt(66) - 3)**

Rizul N.

12/24/12