# How do you solve #7z^2=70z-147#?

##### 3 Answers

See a solution process belowL

#### Explanation:

First, write this equation in standard form by subtracting

Next, divide each side of the equation by

Then we can factor the right side of the equation as:

Now, solve each term on the right side of the equation for

**Solution 1:**

**Solution 2:**

**The Solutions Are:

We could also use the quadratic formula to solve this problem. The quadratic formula states:

For

Substituting:

z = - 3 and z = -7

#### Explanation:

Divide both sides by 7

Solve this quadratic equation by the new Transforming Method (Socratic, Google Search), when a = 1.

Find 2 real roots knowing the sum (-b = 10) and the product (c = 21).

They are: (-3) and (-7)

Here's how to solve this problem rapidly in four easy steps.

#### Explanation:

Given

Solve for

Step 1) Divide all the terms on both sides by 7

Step 2) Set the equation equal to 0.

Subtract

Step 3) Factor

Step 4) Set each factor equal to 0 and solve for

*Don't write this step out if you can just predict the answers by looking at the factors # (z - 3)( z - 7 ).#*

*Just write down the answers and skip this step if you can.*

................

Here's how to find the answers if you can't tell what they will be just by looking at

Set each factor equal to 0 and solve for

Answer:

..............................

Check

Sub each answer into the original equation to make sure it is still an equality,

Sub in 3 in the place of

.

.

Check!

(Testing