Question

Solve the quadratic equation by factoring.
4x² - 20x + 28 = 3

A) x = 5
B) x = 5/2
C) x = 2/5
D) x = - 5/2

Answer 1

Answer:

B)  x = 5/2

Step-by-step explanation:

subtract 3 from each side to get:

4x² - 20x + 25 = 0

this is the difference of 2 squares:

(2x -5)² = 0

one solution, x = 5/2

Answer 2

Answer:

B)  x = 5/2

Step-by-step explanation:

4x² - 20x + 28 = 3

Move terms to the left side

4x² - 20x + 28 - 3 = 0

Subtract the numbers

4x² - 20x + 25 = 0

Use the quadratic formula

$x =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

4x² - 20x + 25 = 0

a = 4

b = -20

c = 25

x = $\frac{-(-20)+\sqrt{(-20)^{2}-4x4x25 } }{2x4}$

Evaluate the exponent

x = $\frac{20+\sqrt{400-4x4x25 } }{2x4}$

Multiply the numbers

x = $\frac{20+\sqrt{400-400 } }{2x4}$

Subtract the numbers

x = $\frac{20+\sqrt{0} }{2x4}$

Evaluate the square root

x = $\frac{20+0 }{2x4}$

Add zero

x = 20 / 2 x 4

Multiply the numbers

x = 20 / 8

Cancel terms that are in both the numerator and denominator

x = 5/2