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.
