Learn how to simplify and solve a Quadratic Equation in few simple and easy steps.

## Step by step guide to Solving a Quadratic Equation

1. Write the equation in the form of: $$ax^2+bx+c=0$$
2. Factorize the quadratic and solve for the variable.
4. Quadratic formula: $$\color{blue}{x=\frac{-b±\sqrt{b^2-4ac}}{2a}}$$

### Example 1:

Find the solutions of each quadratic. $$x^2+7x+10=0$$

$$x^2+7x+10=0$$

You can use factorization method. $$x^2+7x+10=0$$

$$(x+5)(x+2)=0$$
Then: $$(x=-5)$$ and $$(x=-2)$$
You can also use quadratic formula: $$=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=7$$ and $$c=10$$
$$x=\frac{-7±\sqrt{7^2-4.1.10}}{2.1} , x_{1}=\frac{-7+\sqrt{7^2-4.1.10}}{2.1}=-2 , x_{2}=\frac{-7-\sqrt{7^2-4.1.10}}{2.1}=-5$$

### Example 2:

Find the solutions of each quadratic. $$x^2+4x+3=0$$

Use quadratic formula: $$=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=4$$ and $$c=3$$
then: $$x=\frac{-4±\sqrt{4^2-4.1(3)}}{2(1)} , x_{1}=\frac{-4+\sqrt{4^2-4.1(3)}}{2(1)}=-1 , x_{2}=\frac{-4-\sqrt{4^2-4.1(3)}}{2(1))}= \ -3$$

### Example 3:

Find the solutions of each quadratic. $$x^2+5x-6$$

Use quadratic formula: $$=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=5$$ and $$c=-6$$
then: $$x=\frac{-5±\sqrt{5^2-4.1(-6)}}{2(1)} , x_{1}=\frac{-5+\sqrt{5^2-4.1(-6)}}{2(1)}=1 , x_{2}=\frac{-5-\sqrt{4^2-4.1(-6)}}{2(1))}= -6$$

### Example 4:

Find the solutions of each quadratic. $$x^2+6x+8$$

Use quadratic formula: $$=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=6$$ and $$c=8$$
then: $$x=\frac{-6±\sqrt{6^2-4.1(8)}}{2(1)} , x_{1}=\frac{-6+\sqrt{6^2-4.1(8)}}{2(1)}= -2 , x_{2}=\frac{-6-\sqrt{6^2-4.1(8)}}{2(1))}= -4$$

## Exercises

### Solve each equation.

• $$\color{blue}{x^2-5x-14=0}$$
• $$\color{blue}{x^2+8x+15=0}$$
• $$\color{blue}{x^2-5x-36=0}$$
• $$\color{blue}{x^2-12x-35=0}$$
• $$\color{blue}{x^2+12x+32=0}$$
• $$\color{blue}{5x^2+27x+28=0}$$

• $$\color{blue}{x=-2,x=7}$$
• $$\color{blue}{x=-3,x=-5}$$
• $$\color{blue}{x=9,x=-4}$$
• $$\color{blue}{x=7,x=5}$$
• $$\color{blue}{x=-4,x=-8}$$
• $$\color{blue}{x=-\frac{7}{5},x=-4}$$