Complete by solving the square

2x^2-3x-5=0

Simplify the equation into a proper form to complete the square.

2 x^2 - 3x=5

Divide each term in the equation by 2

x^2 - 3x / 2 = 5/2

To create a trinomial square on the left-hand side of the equation, find a value that is equal to the square of half of b, the coefficient of x.

(b/2) ^2 = ( - 3/4) ^2

Now add the term to each side of the equation.

x^2 - 3x / 2 + ( - 3/4) ^2 = 5/2 + ( - 3/4) ^2

Simplify the equation.

x/2 - 3x / 2 + 9/16 = 49/16

Factor the perfect trinomial square into (x - 3/4) ^2.

(x - 3/4) ^2 = 49/16

Solve the equation for x.

x = 5/2, - 1

Ax² + bx + c = 0

2x² - 3x - 5 = 0

2x² + (-3x) + (-5) = 0

x = - b + √b² - 4ac

2a

x = - (-3) + √ (-5) ² - 4 (2) (-5)

2 (2)

x = 3 + √25 + 40

4

x = 3 + √65

4

x = 3 + 8.062257748

4

x = 3 + 8.062257748 x = 3 - 8.062257748

4 4

x = 11.8062257748 x = - 5.062257748

4 4

x = 2.765564437 x = - 1.265564437