2x^2+6x-20

Question

solve by completing the square

Answer 1

Completing the square Method :

The expression is 2x² + 6x - 20.

Take out common factor.

= 2(x² + 3x - 10)

To change the expression (x² + 3x) into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 3. So, (half the x coefficient)² = (3/2)²= 9/4.

Add and subtract 9/4 to the expression.

= 2(x² + 3x + 9/4 - 9/4 - 10)

= 2[{x² + 2(3/2)x + (3/2)²} - (9 + 40)/10]

Apply Perfect Square Trinomial : u² + 2uv + v² = (u + v)².

= 2[(x + 3/2)² - (49/4)]

= 2[(x + 3/2)² - (7/2)²]

Apply Difference of Two Squares : u² - v² = (u + v)(u - v).

= 2(x + 3/2 + 7/2)(x + 3/2 - 7/2)

= 2(x + 5)(x - 2)

The related equation is 2(x + 5)(x - 2) = 0.

Apply zero product property : If a*b = 0, then either a = 0, b = 0 or both a and b are zeros.

x + 5 = 0 and x - 2 = 0

x = - 5 and x = 2.

The value of x = - 5 and x = 2.