Question

Matthew solved the quadratic equation shown

4x2-24x + 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...

Answer 1

Answer:

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:

From the given quadratic expression;

            $4x^{2}$ -24x +7 = 3

           $4x^{2}$ -24x +7 - 3 = 0

            $4x^{2}$ -24x + 4 = 0

Applying the quadratic formula,

 x = (-b ± $\sqrt{b^{2} - 4ac }$) ÷ 2a

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

So that,

 x   = (- (-24)  ± $\sqrt{(-24)^{2} - 4(4*4)}$) ÷ 2(4)

      = (24 ± $\sqrt{576 - 64}$) ÷8

     = (24  ± $\sqrt{512}$) ÷8

    = (24 ± 22.63) ÷8

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

    = $\frac{46.63}{8}$      or   $\frac{1.37}{8}$

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.

Answer 2

The correct solution of the quadratic  equation is; x = 3 ± 2√2.

What is a quadratic equation?

The term quadratic equation has to do with an equation of the sort; ax^2 +  bx + c =0. In this case, we have the equation; 4x^2-24x + 7 = 3.

The equation can be rewritten as; 4x^2-24x + 4 = 0. This implies that the correct solution of the equation is; x = 3 ± 2√2.

Learn more about quadratic equation:https://brainly.com/question/2263981

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