**Step 1.** Write your equation in standard form.

#2x^2 + 16x +42 = 0#

**Step 2.** Move the constant to the right hand side of the equation.

Subtract #42# from each side .

#2x^2+16x +42 -42 = 0-42#

#2x^2+16x = -42#

**Step 3.** Divide both sides of the equation by the coefficient of #x^2#.

Divide both sides by 2.

#x^2 +8x = -21#

**Step 4.** Square the coefficient of x and divide by 4.

#(8)^2/4 = 64/4 = 16#

**Step 5.** Add the result to each side.

#x^2 +8x + 16 =-21 +16 #

#x^2 +8x + 16= -5#

**Step 6.** Take the square root of each side.

#x+4 = ±isqrt5#

**Case 1**

#x_1 + 4 = +isqrt5#

#x_1 = -4+isqrt5#

**Case 2**

#x_2 + 4 = -isqrt5#

#x_2 = -4 -isqrt5 #

So #x = -4+isqrt5# or #x = -4-isqrt5#

**Check:** Substitute the values of #x# back into the quadratic.

**(a)** #x = -4+isqrt5#

#2x^2 + 16x +42 = 2(-4+isqrt5)^2 + 16(-4+isqrt5) +42 = 2(16 -8isqrt5-5) -64 +16isqrt5 +42 = 32 –cancel(16isqrt5) -10 -64 + cancel(16isqrt5) +42= 0#.

**(b)** #x = 4 - isqrt5#

#2x^2 + 16x +42 = 2(-4-isqrt5)^2 + 16(-4-isqrt5) +42 = 2(16 +8isqrt5-5) -64 -16isqrt5 +42 = 32 –cancel(16isqrt5) -10 -64 - cancel(16isqrt5) +42= 0#.