Question

What are the solutions to the quadratic equation of 2x^2-16x+32=0 show work?

Answer 1

2x^2-16x+32=0
2(x^2 - 8x + 16) = 0
2(x - 4)^2 = 0
x - 4 = 0; x = 4

answer
x = 4 is the solution

Answer 2

The Answer is 4

Explanation:

2x² - 16x + 32 = 0

we would multiply 2x² and 32

= 64x²

then factorise 64x² such that the sum of the two nos = -16 AND the product of the nos = 64

the only value that satisfies this condition is -8 (-8 + -8 = -16, and -8 * -8 = 64)

• so our equation becomes

0 = 2x² - 8x -8x + 32

0 = (2x² - 8x) (-8x +32)

• we bring out common terms i.e. factorise it

2x(x - 4) -8(x - 4)

0 = (2x - 8) (x - 4)

0 = 2x - 8 or 0 = x - 4

8 = 2x or 4 = x

x = 8/2 or 4

x = 4 or 4

x = 4

hope it was clear