Which are steps in the process of completing the square used to solve the equation 3 – 4x = 5x2 – 14x? Check all that apply

B)3 = 5x2 – 10x

D)8 = 5(x2 – 2x + 1)

G)  = (x – 1)2

Step-by-step explanation:

Given quadratic : 3 - 4x = 5x2 - 14x

We need to apply completing the square to solve the equation.

First step is to get rid 4x from left side.

We can add 4x on right side to get rid from left side.

3 = 5x^2-14x+4x

On simplifying this step, we get

3 = 5x^2-10x

Now, we need to factor out 5 from right side to get the coefficient of x^2 as 1.

We get,

3 = 5(x^2-2x)

Now, coefficient of x is -2. So, we need to add half of the square of -2.

-2/2 = -1.

And square of -1 is 1.

Therefore, adding 1 inside parenthesis and 5×1 = 5 on left side, we get

3+5 = 5(x^2 -2x+1)

8 = 5(x^2 -2x+1)

Let us find the perfect square of (x^2 -2x+1).

(x^2 -2x+1) = (x-1)^2

Therefore, we get

8 = 5(x-1)^2.

So, the above highlighted are steps in the process of completing the square.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

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