Question

Use the method of completing the square to transform the equation into the equation form (x – p)2 = q. −12 − 5x2 + 2x4 = 0 A) (x2 − 1.25)2 = 6 B) (x2 − 2.5)2 = 6 C) (x2 − 2.50)2 = 7.5625 D) (x2 − 1.25)2 = 7.5625

Answer 1

Given

• -12 -5x² +2x⁴ = 0

Find

• the equation in the form (x -p)² = q

Solution

First of all, recognize that the powers of x are even, so the "x" in the given form will actually be x². The given form has a coefficient of 1 for the squared term (here, x⁴), so we must divide by the coefficient of that term.

... x⁴ - (5/2)x² -12/2 = 0

Putting the constant term on the other side of the equal sign (by adding its opposite), we get

... x⁴ -2.5x² = 6

To complete the square on the left, we add the square of half the coefficient of the "x" term (here, x² term).

... x⁴ -2.5x² +1.25² = 6 + 1.25²

Now we can rewrite the left side to the desired form and add the terms on the right.

... (x² -1.25)² = 7.5625 . . . . . corresponds to D)