# Matthew solved the quadratic equation shown

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## Question:

Matthew solved the quadratic equation shown

4×2-24x + 7 = 3
One of the steps that Matthew used to solve the equation is shown
Step: 4 (2 – A)^2= B
Solution: x =C+/-D
square root of E
Fill in the blanks from the choices below. you may use a number more than once:
2,3,5,6,24,32,36, 148, 154
A should be…
B should be…
C should be…
D should be…
and E should be…

i. A = 6

ii. B = 32 + 32 = 64

iii. C = 3

iv. D = 36 ÷ (6 + 5 + 2) = 2.8

v. E = (148 × 2) + (36 × 6) = 512

Step-by-step explanation:

-24x +7 = 3

-24x +7 – 3 = 0

-24x + 4 = 0

x = (-b ± ) ÷ 2a

We have; a = 4, b = -24 and c = 4.

So that,

x   = (- (-24)  ± ) ÷ 2(4)

= (24 ± ) ÷8

= (24  ± ) ÷8

= (24 ± 22.63) ÷8

x   = (24 + 22.63) ÷8  or (24 – 22.63) ÷8

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=      or

x    = 5.8 or 0.2

Therefore, x = 5.8 or x = 0.2.

From these steps and solution, A = 6, B = 64, C = 3, D = 2.8 and E = 512.

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