How to solve -2x^2-14x+30=0

Question

by completing the square please help i just dont understand how to do this .

Answer 1

Equation is -2x² - 14x + 30 = 0

2x² + 14x - 30 = 0

Separate variables and constants aside by adding 30 to each side 

2x² + 14x = 30

Here x² coefficient is 2, for perfect square make x² coefficient 1 by dividing each side by 2

x²  + 7x = 30/2

x²  + 7x = 15

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

Here x coefficient = 7. So, (half the x coefficient)² = (7/2)²= 49/4
Add 49/4 to each side 

x²  + x + 49/4= 15 + 49/4

(x + 7/2) ²= (60+49)/4

(x + 7/2) ²= 109/4

Take square root both sides 

x + 7/2 = ±√(109/4)

x + 7/2 = ±√109 / 2

subtract 7/2 from each side

x = -7/2 ±√109 / 2

Roots are

x = 1/2 (-7 + √109)

x = 1/2 (-7 - √109)

 

 

Comments

x²  + x + 49/4= 15 + 49/4

Typo in this equation

actual equation is

x²  + 7x + 49/4= 15 + 49/4