CONSTRUCT BY COMPLETING D SQUARE METHOD:-5 ND ¾

To complete the square for the quadratic expression -5x^2 + 3x, follow these steps:

Step 1: Divide the coefficient of the x term by 2, and square the result. (-5/2)^2 = 25/4.

Step 2: Add the value obtained in Step 1 to the expression, and subtract it outside the parentheses to keep the expression balanced:

-5x^2 + 3x + (25/4) - (25/4)

Step 3: Rearrange the terms so that the quadratic term is separated from the linear term:

(-5x^2 + 3x) + (25/4) - (25/4)

Step 4: Factor out the coefficient of the quadratic term (in this case, -5) from the quadratic and linear terms:

-5(x^2 - (3/5)x) + (25/4) - (25/4)

Step 5: Complete the square inside the parentheses by adding the square of half the coefficient of the x term. In this case, the coefficient is (3/5), so (3/5)^2 = 9/25:

-5(x^2 - (3/5)x + (9/25)) + (25/4) - (25/4)

Step 6: Simplify the expression inside the parentheses:

-5((x - (3/5))^2) + (25/4) - (25/4)

Step 7: Combine like terms outside the parentheses:

-5(x - (3/5))^2 + 0

The expression -5(x - (3/5))^2 is the completed square form of the quadratic expression -5x^2 + 3x.