Question

A. Solve by using graphing
⬇️
1. 3x²=6x-3


2. 4x²-12x+9=0

B. Solve by using square root
⬇️
3. 2(x+2)²- 5=9

4. -2x²+=-6

C. Solve by using factoring
⬇️
5. x²-11x= -30

6. f(x)=x²+2x-8

Answer 1

Let's solve the equations as per your request.

### A. Solve by using graphing

1. **\(3x^2 = 6x - 3\)**

Rearranging the equation gives:
\[
3x^2 - 6x + 3 = 0
\]
Dividing through by 3:
\[
x^2 - 2x + 1 = 0
\]
This can be factored as:
\[
(x - 1)^2 = 0
\]
Thus, the solution is:
\[
x = 1
\]

(Note: The graph of \(y = 3x^2\) and \(y = 6x - 3\) will intersect at the point \( (1, 0) \).)

2. **\(4x^2 - 12x + 9 = 0\)**

This can be factored:
\[
(2x - 3)^2 = 0
\]
Thus, the solution is:
\[
x = \frac{3}{2} \text{ (or } x = 1.5\text{)}
\]

### B. Solve by using square root

3. **\(2(x+2)^2 - 5 = 9\)**

Rearranging gives:
\[
2(x+2)^2 = 14 \implies (x+2)^2 = 7
\]
Taking the square root:
\[
x + 2 = ±\sqrt{7} \implies x = -2 ± \sqrt{7}
\]
Thus, the solutions are:
\[
x = -2 + \sqrt{7} \quad \text{and} \quad x = -2 - \sqrt{7}
\]

4. **\(-2x^2 = -6\)**

Dividing through by -2 gives:
\[
x^2 = 3
\]
Taking the square root:
\[
x = ±\sqrt{3}
\]
Thus, the solutions are:
\[
x = \sqrt{3} \quad \text{and} \quad x = -\sqrt{3}
\]

### C. Solve by using factoring

5. **\(x^2 - 11x = -30\)**

Rearranging gives:
\[
x^2 - 11x + 30 = 0
\]
This can be factored as:
\[
(x - 5)(x - 6) = 0
\]
Thus, the solutions are:
\[
x = 5 \quad \text{and} \quad x = 6
\]

6. **\(f(x) = x^2 + 2x - 8\)**

We need to find the zeros (or roots) of the function:
\[
x^2 + 2x - 8 = 0
\]
This can be factored as:
\[
(x + 4)(x - 2) = 0
\]
Thus, the solutions are:
\[
x = -4 \quad \text{and} \quad x = 2
\]

### Summary of Solutions:
1. \(x = 1\)
2. \(x = \frac{3}{2}\)
3. \(x = -2 + \sqrt{7}, \, -2 - \sqrt{7}\)
4. \(x = \sqrt{3}, \, -\sqrt{3}\)
5. \(x = 5, \, 6\)
6. \(x = -4, \, 2\)